{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %matplotlib notebook\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei'] #指定默认字体   \n",
    "plt.rcParams['axes.unicode_minus'] = False #解决保存图像是负号'-'显示为方块的问题\n",
    "# from IPython.core.interactiveshell import InteractiveShell\n",
    "# InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 伯努利分布（Bernoulli Distribution）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "fs=16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcc70f7b8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1,1)\n",
    "p=.8\n",
    "x=[0,1]\n",
    "plt.bar(x,stats.bernoulli.pmf(x,p),label='伯努利-PMF',alpha=.7,width=.2)\n",
    "plt.title('伯努利-概率质量分布',fontsize=fs)\n",
    "plt.xlabel('随机变量',fontsize=fs)\n",
    "plt.ylabel('概率',fontsize=fs)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 二项分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcc7c66a0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1,1)\n",
    "n,p=20,.6\n",
    "binom=stats.binom(n,p)\n",
    "x=np.arange(binom.ppf(0.0001),binom.ppf(.9999))\n",
    "plt.bar(x,binom.pmf(x),label='PMF',alpha=.7,width=.2)\n",
    "plt.title('PMF of 二项分布，B(n={},p={})'.format(n,p),fontsize=fs)\n",
    "plt.xlabel('实验次数',fontsize=fs)\n",
    "plt.ylabel('概率',fontsize=fs)\n",
    "plt.legend(fontsize=fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 泊松分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "mu=10\n",
    "poisson = stats.poisson(mu)\n",
    "x=np.arange(poisson.ppf(0.0001),poisson.ppf(.9999))\n",
    "plt.bar(x,poisson.pmf(x),label='pmf',alpha=0.7,width=.2)\n",
    "plt.title('PMF of 泊松分布，Poisson(mu={})'.format(mu),fontsize=fs)\n",
    "plt.xlabel('平均发生次数',fontsize=fs)\n",
    "plt.ylabel('概率',fontsize=fs)\n",
    "plt.legend(fontsize=fs)\n",
    "plt.subplots_adjust(wspace=0,hspace=.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 二项分布和其他分布的关系"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcca36ba8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3, 1,sharex=True,sharey=True,figsize=(6,7))\n",
    "n,p=1000000,.00001\n",
    "binom=stats.binom(n,p)\n",
    "bx=np.arange(binom.ppf(0.0001),binom.ppf(.9999))\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.bar(bx,binom.pmf(x),label='pmf',alpha=0.7,width=.2)\n",
    "plt.title('PMF of 二项分布，B(n={},p={})'.format(n,p),fontsize=fs)\n",
    "plt.xlabel('实验次数',fontsize=fs)\n",
    "# plt.ylabel('概率',fontsize=fs)\n",
    "plt.legend()\n",
    "\n",
    "mu=10\n",
    "poisson = stats.poisson(mu)\n",
    "px=np.arange(poisson.ppf(0.0001),poisson.ppf(.9999))\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.bar(px,poisson.pmf(x),label='pmf',alpha=0.7,width=.2)\n",
    "plt.title('PMF of 泊松分布，Poisson(mu={})'.format(mu),fontsize=fs)\n",
    "plt.xlabel('平均发生次数',fontsize=fs)\n",
    "# plt.ylabel('概率',fontsize=fs)\n",
    "plt.legend()\n",
    "plt.subplots_adjust(wspace=0,hspace=.7)\n",
    "\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.plot(bx,binom.pmf(x),'.',label='二项分布')\n",
    "plt.plot(px,poisson.pmf(x),label='泊松分布')\n",
    "plt.title('二项分布和泊松分布',fontsize=fs)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 自定义分布函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'概率')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xk=np.arange(7)\n",
    "pk=[.1,.2,.3,.1,.1,.0,.2]\n",
    "custm = stats.rv_discrete(name='custm', values=(xk, pk))\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "plt.bar(xk,custm.pmf(xk),alpha=0.7,width=.2)\n",
    "plt.title('PMF-概率质量分布图',fontsize=fs)\n",
    "plt.xlabel('随机变量',fontsize=fs)\n",
    "plt.ylabel('概率',fontsize=fs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 经验分布函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dccb44240>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xk=np.arange(7)\n",
    "pk=[.1,.2,.3,.1,.1,.0,.2]\n",
    "custm = stats.rv_discrete(name='custm', values=(xk, pk))\n",
    "X1 = custm.rvs(size=20)  # 第一次抽样\n",
    "X2 = custm.rvs(size=200)  # 第二次抽样\n",
    "val1, cnt1 = np.unique(X1, return_counts=True)\n",
    "val2, cnt2 = np.unique(X2, return_counts=True)\n",
    "pmf_X1 = cnt1 / len(X1)\n",
    "pmf_X2 = cnt2 / len(X2)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "plt.plot(xk,custm.pmf(xk),label='PMF')\n",
    "plt.plot(val1,pmf_X1,label='第一次抽样')\n",
    "plt.plot(val2,pmf_X2,label='第二次抽样')\n",
    "plt.title('PMF-概率质量分布图',fontsize=fs)\n",
    "plt.xlabel('随机变量',fontsize=fs)\n",
    "plt.ylabel('概率',fontsize=fs)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 均匀分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x24dcca72b70>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(-1,2)\n",
    "df=pd.DataFrame(data=stats.uniform.cdf(x),index=x,columns=['CDF'])\n",
    "df.plot(title='CDF of uniform dist',legend=True,fontsize=fs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dccc4a630>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 均匀分布，在实际的定义中有两个参数，分布定义域去加你的起点和终点【a,b】\n",
    "a,b=8,16\n",
    "unif=stats.uniform(loc=a,scale=b-a)# loc:该分布的起点，scale：区间的长度，相当于b-a\n",
    "u_rvs=np.linspace(unif.ppf(.01),unif.ppf(.99),100)\n",
    "u_pdf=unif.pdf(u_rvs)\n",
    "df=pd.DataFrame(data=u_pdf,index=u_rvs,columns=['pdf of unif'])\n",
    "df.plot(fontsize=fs,title='pdf of unif({},{})'.format(a,b))\n",
    "r=unif.rvs(1000)\n",
    "plt.hist(r,histtype='bar',density=True,alpha=.2,rwidth=.8,label='rvs of unif({},{})'.format(a,b))\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 指数分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcca920b8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loc,la=0,10\n",
    "exp=stats.expon(loc=loc,scale=1/la)\n",
    "# 指数分布，按照定义只有一个参数lambda，这里的scale = 1/lambda\n",
    "# loc: 定义域的左端点，相当于将整体分布沿x轴平移loc\n",
    "# scale: lambda的倒数，loc + scale表示该分布的均值，scale^2表示该分布的方差\n",
    "exp_rvs=np.linspace(exp.ppf(.001),exp.ppf(.999),num=100)\n",
    "exp_pdf=exp.pdf(exp_rvs)\n",
    "df=pd.DataFrame(data=exp_pdf,index=exp_rvs,columns=['pdf of exp'])\n",
    "df.plot(fontsize=fs,title='pdf of exp({})'.format(la))\n",
    "r=exp.rvs(size=1000)\n",
    "plt.hist(r,histtype='bar',density=True,alpha=.3,rwidth=.8,label='rvs of exp')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcc87fc50>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "loc=0\n",
    "las=[.5,1,2]\n",
    "for la in las:\n",
    "    exp=stats.expon(loc=loc,scale=1/la)\n",
    "    exp_rvs=np.linspace(exp.ppf(.001),exp.ppf(.999),num=100)\n",
    "    exp_pdf=exp.pdf(exp_rvs)\n",
    "    plt.plot(exp_rvs,exp_pdf,label='pdf of exp({})'.format(la))\n",
    "plt.title('pdf of exp',fontsize=fs)\n",
    "plt.xticks(fontsize=fs)\n",
    "plt.yticks(fontsize=fs)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x24dcc90a240>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu,sigma=0,1\n",
    "norm_rvs=np.linspace(-3,3)\n",
    "norm_cdf=stats.norm.cdf(x=norm_rvs,loc=mu,scale=sigma)\n",
    "norm_pdf=stats.norm.pdf(x=norm_rvs,loc=mu,scale=sigma)\n",
    "pf=pd.DataFrame(data=np.array([norm_cdf,norm_pdf]).T,index=norm_rvs,columns=['cdf-Φ of norm','pdf of norm'])\n",
    "pf.plot(fontsize=fs,title='norm({},{})'.format(mu,sigma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dccd57d30>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "norms=[\n",
    "    (0,1),\n",
    "    (0,.5),\n",
    "    (0,2),\n",
    "    (1,1)\n",
    "]\n",
    "for la in norms:\n",
    "    norm=stats.norm(loc=la[0],scale=la[1])\n",
    "    norm_rvs=np.linspace(norm.ppf(1e-5),norm.ppf(.99999),num=100)\n",
    "    norm_pdf=norm.pdf(norm_rvs)\n",
    "    plt.plot(norm_rvs,norm_pdf,label='pdf of norm({},{})'.format(*la))\n",
    "plt.title('pdf of norm',fontsize=fs)\n",
    "plt.xticks(fontsize=fs)\n",
    "plt.yticks(fontsize=fs)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 样本均值的计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29.643327586801306"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=np.random.randint(low=1,high=100,size=19)\n",
    "x# 样本\n",
    "x.mean()\n",
    "stats.gmean(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 样本方差的计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.92072109861539"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 样本\n",
    "x=np.random.randint(low=0,high=100,size=10)\n",
    "x\n",
    "# 计算方差\n",
    "# 直接使用样本二阶中心距计算方差，分母为n\n",
    "np.var(x)# 默认，ddof=0\n",
    "# 使用总体方差的无偏估计计算方差，分母为n-1\n",
    "np.var(x,ddof=1)# 使用ddof设置自由度的偏移量\n",
    "# 计算标准差\n",
    "np.std(x,ddof=0) # 使用ddof设置自由度的偏移量\n",
    "np.std(x,ddof=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 样本均值的期望和方差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9962181572420852 -0.009893428030383492\n",
      "1.0025071548725204 -0.026477450961542873\n",
      "0.6672785103744027 -0.007174587640266762\n",
      "0.5095519820304182 0.005073027085772418\n",
      "0.2007517067505913 0.0022666081914324804\n"
     ]
    }
   ],
   "source": [
    "def mean_and_std_of_sample_mean(ss=[], group_n=100):\n",
    "    \"\"\"\n",
    "    不同大小样本均值的均值以及标准差\n",
    "    \"\"\"\n",
    "    norm_dis = stats.norm(0, 2)  # 定义一个均值为0，标准差为2的正态分布\n",
    "    for n in ss:\n",
    "        sample_mean = []  # 收集每次取样的样本均值\n",
    "        for i in range(group_n):\n",
    "            sample = norm_dis.rvs(n)  # 取样本量为n的样本\n",
    "            sample_mean.append(np.mean(sample))  # 计算该组样本的均值\n",
    "        print(np.std(sample_mean), np.mean(sample_mean))\n",
    "\n",
    "sample_size = [1, 4, 9, 16, 100]  # 每组试验的样本量\n",
    "group_num = 10000\n",
    "mean_and_std_of_sample_mean(ss=sample_size, group_n=group_num)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 大数定理\n",
    "模拟投掷硬币"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "nums=2**np.arange(4,16+1)\n",
    "radios=[]\n",
    "for n in nums:\n",
    "    numheads=0\n",
    "    for i in range(n):\n",
    "        if random.random()>.5:\n",
    "            numheads+=1\n",
    "    radios.append(numheads/(n-numheads))\n",
    "plt.figure()\n",
    "plt.title(\"正反面的比率\")\n",
    "plt.xlabel('单次实验抽样次数')\n",
    "plt.ylabel('比率')\n",
    "plt.plot(nums,radios)\n",
    "plt.hlines(1,0,nums[-1],linestyles=':',colors='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# N重伯努利分布-二项分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcce149e8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEGCAYAAACEgjUUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAHrdJREFUeJzt3XuUnHWd5/H3J+GWC8itDYdb2oxZdUFiSIsJcmkuWQzCqJEBtFdAh426iOzxnDmiiQfWA456vC4zMNMIzmqaOWSHFWTANagE424y0DGGGcMoirlCsElCYoggmu/+8VSnuyvVXb/qruq6PJ/XOXWq+lff5+lvPfXUt5/+PU/9fooIzMystU2odwJmZlZ7LvZmZjngYm9mlgMu9mZmOeBib2aWAy72ZhWQpHrnkKqZcrXac7E3SyTpCuD6eudRgf8t6bX1TsIag4u9NRxJ/0XSFknPSzqr1uuRdLOkPZKek7RB0jUlYk4GPgz83aC2cyX9oCju7ZJ+Kek3kt4xqP3dkjZJekrS6Qm5f0TSNkm9kl5XJvY4SS8X4rdJWlZ46nPAneV+l+WD/KUqazSSdgKnAduASRGxu5brkXQzcFhE3CjpBOBnwJsi4oVBMf8A/I+I+Gnh5zOA7wBPR0Rnoe0Q4BngKmAd8CNgHjAVWA+cC7wM3BsRHSPk/Wbg/wBvBaYDSyLinSPEvwN4T0R8uMRzfwv8U0Q8Otzylg8+srdGdGREbI6IV0db6Ee7nojYCmwF/qy/TdKhwPT+Ql/wUeAzRYu/DdgcET+KiO3AD4GzgIuARyLi5xHxa2CTpP8wQhrvBr4VEc9GxCrgWElTRoifTfYHqpRu4MoRlrWccLG3mil0jzxY6LrYJOnSQvsGSfcUuk3+WtJvJV0l6QuSthVitkn6ecLv+KvCun8haUGhreL1DFrffwROBJ4e1DwDeKoo9ENkR/GDnQg8OejnjcDrR2gfTnH8s2RH+MOZDfxVYTuuHvyHJCLWASP9YbGccLG3WjsFOBO4FLhb0uRC+8PA/wXagM8CnRHxyYg4DiAijouIU0ZasaQLgauBWcB7gG9Kmlbpego+Jul54OfAbRGxY9BzRwE7BwdH6f7PicDg/yBeAo4coX04lcY/A1wWEa8F/gn4StHzvirHXOyt5u6PiJ2FI8znGTjKXAXsGXQ/mn1xAbC0sP71wL8AZ48yz7+JiGlkR9zXSjpn0HPbgWMS1rGToUV5ErBvhPZK11NSRNw4qIvpduD8/ucKl1/6xJy52FvNDT6qnMBA0fpT0f1oRdHjMRW2Qp/6KrL+937PAG9KWHxN0XIdwBagl+xEbXH7cPbHF4r16WTnEQ4g6RBJVw1qOgH406Br7N9K9t+K5ZyLvdXauyUdJWk22dHx0+UWqMD3gC5JR0p6I1mh/clYVijpOGAu8Iv+toh4FXiq3GWgEbEN6JO0RNJ7gXcCjwCPAzMlXStpEdl/D4+XeV3vkbSQ7CTw9ojYPMzv/APwaUmdko4sxH93UDfTR4GlZV+4tTwXe6u1tWQF+AHgQxHx+2qtOCJ+AHyb7GTmdwvrf36Uq+vvs18L3As8WPT8TcBfSzq8zHr+M/AWYAnwwYh4vlB43wVcTnZi972FIt1/AvnQote1G7gM+ATZ5ZpdhdgzJT1U4nd+iOx6+l+T9fdfX4ifDxwSEasTXr+1OF9nbzVTuH6diLi5vplUh6QLgD+LiO4qrvMLEfHJaq2vaN13Af8tIn5Xi/Vbczmo3gmYNYuI+CHZtfPVVPwfRNVExF/Wat3WfHxkb2aWA+6zNzPLARd7M7McaJg++2OPPTba29vrnYaZWVNZs2bNCxHRVi6uYYp9e3s7vb299U7DzKypSNqYEuduHDOzHHCxNzPLARd7M7McaJg+ezMbm1dffZUtW7bw8ssv1zsVq4HDDjuME088kYMPPnhUy7vYm7WILVu2cPjhh9Pe3s7AoJfWCiKC7du3s2XLFl73uhGnJB5WUjeOpLskrZK0JDWmMNLhw4UJk/9+VNmZNZieHmhvhwkTsvuennpnNODll1/mmGOOcaFvQZI45phjxvRfW9liXxhmdWJEzANmSJqZGPMBoKcwsfLhkoadYNmsGfT0wKJFsHEjRGT3ixY1VsF3oW9dY31vU47sO4FlhcfLySZQTonZDpxaGGP7JOCA8bglLSoc+ff29fVVlrnZOFu8GPbuHdq2d2/WbtboUor9FAZmydkBTEuM+QnZJMkfJ5useUfxQhHRHREdEdHR1lb2C2BmdbVpU2Xt1tg2bNhQ7xSGeOaZ4vnrqyul2O8hmwMTYOowy5SKuQn4SER8Fvh34INjS9Wstsr1x598cunlitsbuV9/sGbJsxa+8IUv8NOf/rR84Dh68MEHueeee2q2/pRiv4aBrptZwIbEmKOAN0uaSDZdnMdStoaV0h9/660wefLQ5SZPztorWU8jqHeeu3bt4vzzz6ezs5PvfOc7VV/2mmuuYfbs2XR2dnLFFVfwpz8NTHW8YcMGNm/ezMKFCwF4/vnnOfvsgXnqX331VS699FLe/va3c/fddw/bVkpq3NatWznxxBPp7Oyks7OTvr4+brjhBh566CF+97sazTUTESPegCOAdcBXyLpjZgG3lIl5DXAG2UTHe8jm4Zw60u+ZM2dOmNXL9OkRWdkbeps+fWjc0qVZm5TdL106uvXUwvr165Nj65lnRMRjjz0WixcvrtmyV199daxcuTIiIj784Q/Hww8/vP+5z372s/u31Y4dO+Kiiy6K2bNn73/+y1/+ctx0000REbFgwYLYvXt3ybZSUuPuu+++uP322w9of/jhh+Nb3/rWsK+r1HsM9EaZOh4R5Y/sI5sPsxNYDZwXEesiYkmZmF0R8XhEnBIRUyNifkTsGePfJbOaSe2P7+qCDRtg377svqtrdOupt1rkefPNN7NgwQLOPfdcLrvsMv74xz/S2dnJ+9//fi644AIuuOACPvWpT/H1r3+dj3/84yxdunT/UW0pr7zyCu973/s499xz6erq4g9/+EPysoO98MILTJkyZf/Pv/71r3nTm94EwMSJE7n33ns54ogj9j+/YsUKLr/8cgDOOeccent7S7aVkhq3evVqvvGNb3D66afz6U9/en/73LlzWbt2bdnXNBpJ19lHxM6IWBYR28YSY9aoUvvjx2s9tVarPM8++2wee+wxpk2bxgMPPADA5z73OTZv3swDDzzA6tWrueGGG/ja177GNddcw4oVKxju4ow777yTU089lccee4yZM2dy9913Jy8LcP311/PGN76RZ599lnnz5pWMOeKII3jNa14zpO2ll17ihBNOAODoo4/m+eefL9lWSmrcggULWLFiBU888QSrVq3iySefBGDSpEn8/ve/H/Y1jYXHxjEjrT9+PNdTa7XKc86cOQCcdtpp+692aW9v5/jjj2fq1Kn93b5J1q9fz9ve9jYgO+J96qmnKsrltttuY/369bz1rW/l85///P72SZMmsWfP8B0NU6dO3V9w9+zZw759+0q2pS5byplnnsnhhx/OxIkTmT17Nk8//TQAv/nNbzjppJMqep2pXOzNyLpjurth+nSQsvvu7gO7acZrPbVWqzwff/xxANauXcvrX//6Ma3rlFNOYfXq1UDW7XHKKadUvI4JEyZw1FFHDTnpefHFF3PfffcNu8ycOXP4yU9+AsC6detob28v2Za6bCkXXXQRzz33HHv37mX58uWceuqpACxbtoxLLrmk0peZxGPjmBV0dVWnKFdrPbVWizyfeOIJOjs7Oe6447jkkkv46le/Oup1XXvttVxzzTWcc845nHTSSUP6tlNcf/31TC78+zL4ksZLLrmEK664ggULFvDa1772gOWuvvpqLr74YlauXLn/v4sTTjjhgLY1a9bwyCOPcOONN4647I9+9CPWr1/Pxz72sf1xN910E+eddx6HHHIIH/nIR3jDG97AL3/5S7Zu3cppp51W6aZKk3IWdzxuvhrHbGwquRqnFm666aZ49NFH65pDqs2bN0dPT8+wz2/dujXuvffeePHFF4dt2759e3zzm99MWjbFHXfcEbt27RoxZixX4ygq6EOrpY6OjvC0hGaj99RTT+2/ysRq75VXXmHixIkcdND4dZCUeo8lrYlsDLIRuRvHrIVEhAdDGyeHHnrouP6+sR6Y+wSt5UajDA9QqzwOO+wwtm/fPuaiYI0nCuPZH3bYYaNeh4/sLRf6hwfoH7Wyf3gAGN+TqbXM48QTT2TLli1JXzSy5tM/U9Vouc/ecqG9PSusxaZPz74Jm7c8rHWk9tm7G8dyoVGGMWiUPCx/XOwtFxplGINGycPyx8XecqFRhjFolDwsf1zsLRcaZRiDRsnD8scnaM3MmphP0JqZ2X4u9mZmOZBU7CXdJWmVpCWpMZI+KmlF4fYzSX9fraTNzKwyZYu9pIXAxIiYB8yQNDMlJiLuiIjOiOgEVgJ3Vjl3MzNLlHJk3wksKzxeDpxVSYykE4BpEXHA2VdJiyT1Sur1V7zNzGonpdhPAbYWHu8AplUYcx1wR6kVR0R3RHRERMdIc0mamdnYpBT7PcCkwuOpwyxTMkbSBOA8YMWYsjQzszFJKfZrGOiWmQVsqCDmbOBfolEu5jczy6mUIY7vB1ZKOh5YAFwp6ZaIWDJCzNxC+0XAj6uZsJmZVa5ssY+I3ZI6gfnAFyNiG7CuTMyuQntlMwSbmVlNJF1nHxE7I2JZodCPOsasVhplFqpqabXXY/Xnmaqs6TXKLFTV0mqvxxqDB0Kzptdqsz+12uux2vJAaJYbrTb7U6u9HmsMLvbW9Fpt9qdWez3WGFzsrem12uxPrfZ6rDG42FvTa7XZn1rt9Vhj8AlaM7Mm5hO0Zma2n4u9mVkOuNibmeWAi72ZWQ642JuZ5YCLvZlZDrjYm5nlgIu9mVkOuNibmeVAUrGXdJekVZKWVBoj6XZJl441UTMzG72yxV7SQmBiRMwDZkiamRoj6WzguIh4sMp5m5lZBVKO7DuBZYXHy4GzUmIkHQzcCWyQ9K5SK5a0SFKvpN6+vr5K8jYzswqkFPspwNbC4x3AtMSYq4D1wBeBMyRdX7xQRHRHREdEdLS1tVWau5mZJUop9nuASYXHU4dZplTMbKC7MAH5UuC8saVqeeXJt0vzdrFKpBT7NQx03cwCNiTG/AqYUWjrAErMqmk2sv7JtzduhIiBybfzXti8XaxSZcezl3QEsBL4IbAAuBL4i4hYMkLMXGAfcDdZl87BwGURsZVheDx7K8WTb5fm7WL9UsezT5q8RNJRwHzgx4VumVHFjMTF3kqZMCE7ci0mwb59459Po/B2sX5VnbwkInZGxLKRinhKjFmlPPl2ad4uVil/g9YamiffLs3bxSrlYm8NzZNvl+btYpXyhONmZk3ME46bmdl+LvZmZjngYm9mlgMu9mZmOeBib2aWAy72ZmY54GJvZpYDLvZmZjngYm9mlgMu9mZmOeBib2aWAy72ZmY54GJvZpYDScVe0l2SVklakhoj6SBJmyStKNzeXK2kzcysMmWLvaSFwMSImAfMkDQzMeY04B8jorNw+9dqJ29mZmlSjuw7gWWFx8uBsxJj5gKXSHq8cNR/UPFCkhZJ6pXU29fXV2nuZmaWKKXYTwG2Fh7vAKYlxjwBXBgRZwAHAxcXLxQR3RHREREdbW1tleZuLaKnB9rbs0m029uzn606vG2t3wFH2yXsASYVHk+l9B+IUjFPRsQrhbZe4IDuH7OeHli0CPbuzX7euDH7GTzF3lh529pgKUf2axjoupkFbEiM+bakWZImAu8G1o0pU2tJixcPFKN+e/dm7TY23rY2WMqR/f3ASknHAwuAKyXdEhFLRoiZCzwJ3AMI+G5E/KC6qVsr2LSpsnZL521rg5Ut9hGxW1InMB/4YkRso+govUTMLmAX2RU5ZsM6+eSse6FUu42Nt60NlnSdfUTsjIhlhUI/6hizYrfeCpMnD22bPDlrt7HxtrXB/A1aq6uuLujuhunTQcruu7t9ArEavG1tMEVEvXMAoKOjI3p7e+udhplZU5G0JiI6ysX5yN7MLAdc7M3McsDF3swsB1zszcxywMXezCwHXOzNzHLAxd7MLAdc7M3McsDF3swsB1zszcxywMXezCwHXOzNzHLAxd7MLAdc7M3MciCp2Eu6S9IqSUsqjZE0TdLasSZqZmajV7bYS1oITIyIecAMSTMrjPkSMKlaCVtz6emB9naYMCG77+mpd0Y2mN+f/Eg5su8ElhUeLwfOSo2RdD7wElByqkJJiyT1Surt6+tLz9qaQk8PLFqUzYMakd0vWuSC0ij8/uRLSrGfAmwtPN4BTEuJkXQI8BngxuFWHBHdEdERER1tbW3pWVtTWLwY9u4d2rZ3b9Zu9ef3J19Siv0eBrphpg6zTKmYG4HbI+LFsSZpzWnTpsrabXz5/cmXlGK/hoGum1nAhsSYC4HrJK0A3iLpG2NJ1JrPySdX1m7jy+9PvqQU+/uBD0j6CnA58HNJt5SJeSgizomIzojoBH4WEddWM3FrfLfeCpMnD22bPDlrt/rz+5MvZYt9ROwmOwG7GjgvItZFxJIyMbuKnu+sUr7WRLq6oLsbpk8HKbvv7s7arf78/uSLIqLeOQDQ0dERvb299U7DzKypSFoTER3l4vwNWjOzHHCxNzPLARd7M7MccLE3M8sBF3szsxxwsTczywEXezOzHHCxNzPLARd7M7MccLE3M8sBF3szsxxwsTczywEXezOzHHCxNzPLARd7G7WeHmhvhwkTsntPVN2a/D63hoNquXJJRwNzgLUR8UItf5eNr54eWLRoYMLqjRuzn8GTX7QSv8+tI+nIXtJdklZJWpIaI+ko4J+BM4BHJbVVJWNrCIsXDxSAfnv3Zu3WOvw+t46yxV7SQmBiRMwDZkiamRhzGvCJiLgV+D5wenVTt3ratKmydmtOfp9bR8qRfSewrPB4OXBWSkxEPBYRqyWdQ3Z0v6p4IUmLJPVK6u3r66s0d6ujk0+urN2ak9/n1pFS7KcAWwuPdwDTUmMkCbgC2Am8WrxQRHRHREdEdLS1uZenmdx6K0yePLRt8uSs3VqH3+fWkVLs9wCTCo+nDrNMyZjIXAc8Cfz52FK1RtLVBd3dMH06SNl9d7dP2rUav8+tI+VqnDVkXTergVnAL1JiJH0SeC4ivgUcCbxYlYytYXR1+UOfB36fW0NKsb8fWCnpeGABcKWkWyJiyQgxc8mO7pdJuhb4N7K+fDMzq4OyxT4idkvqBOYDX4yIbcC6MjG7Ck/Nr266ZmY2GklfqoqInQxcbTPqGDMzqw8Pl2BmlgMu9mZmOeBib2aWAy72ZmY54GJvZpYDLvZmZjngYm9mlgMu9mZmOeBib2aWAy72NizPPWqpvK80vprOQWvNy3OPWirvK81BEVHvHADo6OiI3t7eeqdhBe3t2Ye22PTpsGHDeGdjjcz7Sn1JWhMRHeXi3I1jJXnuUUvlfaU5uNhbSZ571FJ5X2kOLvZWkucetVTeV5pDUrGXdJekVZKWpMZIeo2k70laLuk7kg6pVtJWe5571FJ5X2kOZYu9pIXAxIiYB8yQNDMxpgv4SkT8J2Ab8I7qpm611tWVnWDbty+794fXhuN9pfGlXHrZycAMVMvJJhZ/ulxMRNw+6Pk24LfFK5a0CFgEcLI7+MzMaialG2cKsLXweAcwrZIYSfOAoyJidfFCEdEdER0R0dHW1lZR4mZmli7lyH4PMKnweCql/0CUjJF0NHAb8N6xpWlmZmORcmS/hqzrBmAWsCElpnBC9n8Bn4qIEl+5MDOz8ZJS7O8HPiDpK8DlwM8l3VIm5iHgL4HTgcWSVki6oop5m5lZBZKGS5B0FDAf+HFEbBttzEg8XIKZWeVSh0tIGggtInYycLXNqGPMzKw+/A1aM7MccLHPKY8/buPJ+1v9eTz7HPL44zaevL81Bo9nn0Mef9zGk/e32vJ49jYsjz9u48n7W2Nwsc8hjz9u48n7W2Nwsc8hjz9u48n7W2Nwsc8hjz9u48n7W2PwCVozsybmE7RmZrafi72ZWQ642JuZ5YCLvZlZDrjYtyCPQ2LNyPttbXlsnBbjcUisGXm/rT1fetliPA6JNSPvt6NX1UsvJd0laZWkJZXESJomaWVaylYNHofEmpH329orW+wlLQQmRsQ8YIakmSkxhWkK/ycwpdpJ2/A8Dok1I++3tZdyZN/JwHSDy4GzEmP+BFwB7B5uxZIWSeqV1NvX15eYso3E45BYM/J+W3spxX4KsLXweAcwLSUmInZHxK6RVhwR3RHREREdbW1tqTnbCDwOiTUj77e1l3I1zh5gUuHxVEr/gUiJsXHS1eUPiTUf77e1lVKU1zDQdTML2DDKGDMzq5OUI/v7gZWSjgcWAFdKuiUilowQM7f6qZqZ2WiVPbKPiN1kJ2BXA+dFxLqiQl8qZteg5zqrmG/u+VuGlmfe/0cv6Ru0EbGTgattRh1jY+NvGVqeef8fG3+Dton4W4aWZ97/S/PkJS3I3zK0PPP+PzYu9k3E3zK0PPP+PzYu9k3E3zK0PPP+PzYu9g1mpKsN/C1Dy7OU/d9X6wzPJ2gbSPHVBpAdubigm5WX189P6glaF/sG4qsNzEYvr58fX43ThHy1gdno+fMzMhf7cVSuP9FXG5iNXurnJ6/9+i7246S/P3HjRogY+Pbf4B3NVxuYjV7K5yflc9iyIqIhbnPmzIlWNn16RLZ7Db1Nnz40bunSrE3K7pcuHf9czZpVuc9P6uewmQC9kVBjfWRfJeX+NUztT+zqyk4m7duX3bfyVQRm1Vbu85P6OWzFrh4X+ypI+dfQ/fFm9ZfyOWzVrh4X+0Qj/aVfvHjotb2Q/bx48cDP7o83q7+Uz2HK5xma8Og/pa9nPG717LMv18+3dGnE5MlD+/gmTx6Ik0r3A0qV/R4zq71yn8OUz3O5mpDye6qFxD77uhf5/ttoi31KoR5LIY8of1KnFU/6mOVVyue5XExKXemPG+sfhKoWe+AuYBWwpJKYlOX6b6Mp9uU2aDUKeUT5v/Spb6yZNb6Uz3O5mpBSV6pVN6pW7IGFwD8UHt8NzEyJSVlu8G00xb4aR9wp/7KlvnHuojFrDWO9hLNadSVFarFPOUHbycB0g8uBsxJjyi4naZGkXkm9fX19CakMVe4yqpTLrFLOzqec1PElk2ato9znuVxNSKkr4z28Q0qxnwJsLTzeAUxLjCm7XER0R0RHRHS0tbVVkjdQfoNWs5B7aGEz61euJqTUlfG+HDul2O8BJhUeTx1mmVIxKcuNSbkNWs1C7iN3MxtspJqQUlfG+3LslAK8hoEumFnAhsSYlOXGpNwGdSE3s3opV1fGu8eg7Hj2ko4AVgI/BBYAVwJ/ERFLRoiZC0RxW0TsGu73eDx7M7PKVW08+4jYTXaydTVwXkSsG1zoh4nZVaqt0hdhZmbVcVBKUETsZODKmuSYlOXMzKz2PDaOmVkOuNibmeWAi72ZWQ6UvRpnvEjqA0rMDd9wjgVeqHcSiZopV2iufJspV2iufJspV6h/vtMjouy3Uhum2DcLSb0plzk1gmbKFZor32bKFZor32bKFZonX3fjmJnlgIu9mVkOuNhXrrveCVSgmXKF5sq3mXKF5sq3mXKFJsnXffZmZjngI3szsxxwsS9D0tGS5ks6tt65mJmNlov9CCQdBfwzcAbwqKQ2SZskrSjc3lznFA8gaZqktYXHd0laJWlJueXqpT9fSQc16rYtlZuk/y7pCUl/W+/8ig2T788G/Ty/3jkWk3S7pEsLj5thv71d0qWNvN8Wc7Ef2WnAJyLiVuD7wIeAf4yIzsLtX+ubXklfAiZJWghMjIh5wAxJM+uc13C+RDbJzWk07rYdkhtwCNlcDWcAv5V0YT2TK6E432eBfx+0bR+pb3pDSTobOC4iHmyG/XZwvjT2fjuEi/0IIuKxiFgt6RyyD/bvgUskPV44+kgaNXS8SDofeAnYRtrcwXVVlO9cGnfbDskNuAC4rzDZ8/eBs+ua3YGK8307cIak/yfpfkmH1zm//SQdDNwJbJD0Lhp8vy2RbyPvt0O42JchScAVwE5gLXBhRJwBHAxcXM/cBpN0CPAZ4MZCU8rcwXVTIt8naNBty4G5TaKBty0H5tsOXBQRZwJPAh+sY27FrgLWA18kO6C6jsbetsX5HkPj7rdDuNiXEZnryD4kx0fEc4WneoFG+hfzRuD2iHix8HPN5wAeo+J8n2zgbVucW6Nv2+J8JwG/GvRzI23b2UB3RGwDlgI/prG3bXG+pzfwfjtEo23IhiLpk5KuKvx4JPB3kmZJmgi8G1hXv+wOcCFwnaQVwFuAS6nxHMBjVJzv9xp42367KLcpNPa2Lc73SrL9AeAyGmvb/gqYUXjcQfZfSCNv2+J8aeD9dgh/qWoEhatxlgGHAv8G3AH0AAK+GxGL65jesAoF9M+pYA7geirk+zHgHhpw20o6lUG5kXU/rSQ7knsH8I6I+E39MhyqRL5/A9xP9kdqFfBfI+LV+mU4oHD+4G6y7pqDyf4wfZcG3W9L5HsjcBsNuN8Wc7FvYYU/VvOBHxf+7bQqkTQJeCfw04h4pt75tBLvt7XhYm9mlgPuszczywEXezOzHHCxNzPLARd7M7MccLE3M8uB/w8s6IeLpf9eagAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n,p=100,.5\n",
    "b=stats.binom(n,p)\n",
    "b_rvs=np.arange(b.ppf(.0001),b.ppf(.9999))\n",
    "plt.figure()\n",
    "plt.plot(b_rvs,b.pmf(b_rvs),'bo',label='pmf of B({},{})'.format(n,p))\n",
    "plt.title('pmf of B({},{})'.format(n,p))\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# N重伯努利分布-近似正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dcce85278>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu,sigma=100*.5,(100*.5*(1-.5))\n",
    "norm=stats.norm(loc=mu,scale=sigma)\n",
    "norm_rvs=np.linspace(-20,120)\n",
    "plt.figure()\n",
    "plt.plot(norm_rvs,norm.pdf(norm_rvs),label='pdf of N({},{})'.format(mu,sigma))\n",
    "plt.title('pdf of N({},{})'.format(mu,sigma))\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 模拟服从各分布的随机变量和"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义分布类型\n",
    "drv,crv=0,1# 离散型分布，连续型分布\n",
    "# 绘制连续型随机变量和的分布\n",
    "def  sampling2pdf(plt,n,dist,t=10000):\n",
    "    \"\"\"\n",
    "    :param plt: 为绘制对象\n",
    "    :param n: 单次实验的抽样次数\n",
    "    :param dist:独立同分布的分布对象\n",
    "    :param t:独立同分布的实验次数\n",
    "    \"\"\"\n",
    "    sum_of_samples=np.zeros(t)\n",
    "    for i in range(t):\n",
    "        samples=dist.rvs(size=n)# 抽样次数\n",
    "        sum_of_samples[i]=np.sum(samples)\n",
    "    plt.hist(sum_of_samples,density=True,bins=100,label='{}RVS'.format(n),color='#348ABD')\n",
    "# 绘制离散型随机变量和的分布\n",
    "def sampling2pmf(plt,n,dist,t=10000):\n",
    "    sum_of_samples=np.zeros(t)\n",
    "    for i in range(t):\n",
    "        samples=dist.rvs(size=n)\n",
    "        sum_of_samples[i]=np.sum(samples)\n",
    "    val,cnt=np.unique(sum_of_samples,return_counts=True) # 独立同分布的随机变量和的值以及对应的个数\n",
    "    pmf=cnt/len(sum_of_samples)\n",
    "    plt.vlines(val,0,pmf,linestyles='-',lw=3,color='#348ABD')\n",
    "def plot(n,dist,subplot,plt,t,dist_name,dist_type):\n",
    "    \"\"\"\n",
    "    :param dist_name: 分布名称\n",
    "    :param dist_type: 分布类型\n",
    "    \"\"\"\n",
    "    plt.subplot(subplot)\n",
    "    sampling2pmf(plt=plt,n=n,dist=dist,t=t) if dist_type==drv else sampling2pdf(plt,n,dist,t)\n",
    "    # 正态分布\n",
    "    mu,sigma=n*dist.mean(),(n*dist.var())**.5\n",
    "    norm=stats.norm(loc=mu,scale=sigma)\n",
    "    norm_x=np.linspace(mu-3*sigma,mu+3*sigma,t)\n",
    "    norm_pdf=norm.pdf(norm_x)\n",
    "    plt.plot(norm_x,norm_pdf,'r--',alpha=.5,label='N(${0:.0f},{1:.2f}^2$)'.format(mu,sigma))\n",
    "    plt.legend(loc='upper left',prop={\"size\":6})\n",
    "size=[\n",
    "(1,231),\n",
    "(4,232),\n",
    "(20,233),\n",
    "(80,234),\n",
    "(200,235),\n",
    "(1000,236),\n",
    "]# 抽样次数,画布位置\n",
    "t=10000# 实验次数\n",
    "# dist_name,dist_type='伯努利',drv\n",
    "# dist=stats.bernoulli(p=.99)# 定义一个伯努利分布\n",
    "# dist_name,dist_type='二项分布',drv\n",
    "# dist=stats.binom(n=20,p=.4)# 定义一个二项分布\n",
    "dist_name,dist_type='均匀分布',crv\n",
    "dist=stats.uniform(loc=3,scale=5-3)# 定义一个均匀分布\n",
    "plt.figure(figsize=(8,4))\n",
    "for i in size:\n",
    "    plot(n=i[0],dist=dist,subplot=i[1],plt=plt,t=t,dist_name=dist_name,dist_type=dist_type)\n",
    "plt.suptitle('t次{}实验的RVS和收敛于正态分布'.format(dist_name))\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0,right=1,top=.93,bottom=0.05)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 卡方分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dce6f9da0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "df=20# 卡方分布的自由度\n",
    "chi2=stats.chi2(df=df)\n",
    "chi2_x=np.linspace(chi2.ppf(1e-3),chi2.ppf(.999),200)\n",
    "plt.plot(chi2_x,chi2.pdf(chi2_x),'r-',lw=5,alpha=.6,label=r'PDF of $\\chi^2$({})'.format(df))\n",
    "chi2_rvs=chi2.rvs(size=10000)\n",
    "plt.hist(chi2_rvs,density=True,histtype='stepfilled',alpha=.2)\n",
    "plt.ylabel(\"概率\")\n",
    "plt.title(r'PDF of $\\chi^2$({})'.format(df))\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dce77ef60>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XNPtq4cKFTJ06lexs355XmjFjBvfeey/p6ekXrFVKS0tj1apVHDx4kBMnTjBhQteshDHW2i65UbCkpqbaHTt2dMu9tx44wyd7T/M/7x7XfDq8iIhcfvbv33/BAt6+7uWXX+bTTz/lhRdeID09nT179vh0XV5eHtu2bWP27NmXvLdy5Upmz55NTEyMz3W09O9ijNlprU1t71qNAPmh+UT4ugYFIBER6RMOHTrEiy++SFZWFrGxsSQkJDBt2rRWd34+X1JSUovhB7jgibGuoADkh/NPhI8M7eZiREREusDIkSM5cOBA8/ebN29uo3XPpWELP7gbR4B0HIaIiEjvogDkh6YApCfBREREehcFID80T4FpBEhERKRXUQDyg/u8RdAiIiLSeygA+UEBSEREpHdSAPJDqNMJaApMRESkt1EA8oNGgERERHonBSA/uJze4y8UgERERHoXBSA/hDgdOB2aAhMREQHYsGEDjzzyCHfffXerO0Pn5ub63N+RI0cCVNmlFID85HY6tQ+QiIgIMHPmTDIyMli9ejVvvfXWJe8vW7aMXbt2+dzfhx9+yLp16wJZYjMFID+5QxzUKgCJiEiQLV26lDFjxjBlyhRuv/128vPzWbBgASkpKaSmppKRkXFBu7S0NNLS0li+fHmH7lNSUsLUqVNJS0vj/fff71Stzz33HI899tgFr+Xm5nL8+HFmzZoFwOnTp7n11lsvaLNw4UJuuukmnnvuOQAWL17Mxo0bKSsr61QdbVEA8pPbaTQFJiIiXWLJkiVs27aNBx98kJdeegmA5cuX8/HHH/Pss8+Sk5PT3C4zM5PMzEwef/zxDt0jOzubm2++mczMTO65554W21RUVJCYmMjTTz8NwBdffEFKSgpVVVU89dRTpKenM2nSpAuuWbt2bXMoKioqYv78+VRUVDS//95771FfX8/nn3/OkSNHOHToEABz585lw4YNHfoZfKEA5KdQl1OLoEVEpEsVFRURHh7e/H1cXBx33XUX27Zt87mPmpoa7r//fm677TbmzJmDx+Ph17/+NYsWLeL1118nLS2NgoKCFq+NjIwkJyeH9evXU1lZyUMPPcTq1avJyMhgy5YtvPPOO6xcufKCaw4fPsyYMWMAcDqdvPXWW8TExDS/n5mZyU9/+lMApk2bxvbt2wGYPHkyu3fv9vnn8pVOg/eTy2kUgERE+pA/5/6Z0xWnA9rn4MjB3DnsznbbPf/887zyyiskJyezYsUKFi9e3PxeXFwcxcXFze1WrVrF2LFjWbFiRYt9ZWRkMH78eNavX8/SpUt59dVXWbx4MRMnTiQzM5OlS5e2WUtcXBwREREsXLiQefPmkZKSQkpKCosWLWr35zg/+DRpGlUCGDBgQPNaofDwcKqqqtrts6MUgPzkdjqo8NR3dxkiItIHLFmyhLlz57b4XmFhIUlJSZw5c6bNdk327dvXvB5n8uTJbNq0qcP1TJgwgZMnT/LGG2+02zY8PJzy8nKioqJafD8qKqo56JSXl9PQ4B1cOHr0KMnJyR2urT0KQH5yhzgprKzt7jJERKSL+DJS09WKi4vZtGkTTz75JG+++aZP14wbN46srCzuuOMOsrKyGDduXIfuWVBQwNatW3nmmWdwONpfUTN9+nTeffdd5s+f3+L7119/Pdu3b2fy5MlkZ2czatQoAN5+++1W1yL5QwHIT+4Qh6bARESk2zzxxBOEhoaybNkyRo8e7fN1Dz/8MAsWLGDKlCkkJyc3L2j21cKFC5k6dSrZ2dk+tZ8xYwb33nsv6enpDBo06JL3Z86cya233kp+fj6bNm0iKyuLgwcPcuLECSZMmNCh2nxhrLUB77Qrpaam2h07dnTb/T/IzufLb4v5Hz8a2201iIhIcO3fv795Aa/Ayy+/zKeffsoLL7xAeno6e/bs8em6vLw8tm3bxuzZs1t8v6ioiM2bNzNlyhSGDBnCypUrmT17dotrhqDlfxdjzE5rbWp7tWgEyE9up6FWj8GLiEgfcejQIV588UWysrKIjY0lISGBadOmtbrz8/mSkpJaDT8AsbGxzU+CATz66KMBqbklCkB+Cg1xUtdgqW+wOB2mu8sREREJqpEjR3LgwIHm7zdv3tyN1XSe9gHyk8upE+FFRER6GwUgP7lDGgOQpsFERER6DQUgP4U2BqCaOu0FJCIi0lsoAPkpzOUEoKZWI0AiIiK9hQKQn8IbA1BVrUaAREREegsFID+Fub2/wiodhyEiItJrKAD5qWkEqFIBSEREpNdQAPJTUwCq1iJoERGRXiNoAcgY8ztjzOfGmGdaeb+fMWaTMeYTY8z7xhi3L9f1NCFOBy6noVojQCIiIr1GUAKQMWYW4LTW3gSMMMaMbKHZHOBFa+004BRwp4/X9TjhbqemwEREpM/bsGEDjzzyCHfffXerR2Pk5ub63N+RI0cCVNmlgjUClAa83fj1J8AtFzew1q6w1jbtnx0PnPHlOgBjzM+MMTuMMTsKCgoCWHbnhIU49RSYiIj0eTNnziQjI4PVq1fz1ltvXfL+smXL2LVrl8/9ffjhh6xbty6QJTYLVgCKBE40fl0IDG6toTHmJiDWWpvl63XW2lestanW2tT4+PjAVd1J4W4n1QpAIiISREuXLmXMmDFMmTKF22+/nfz8fBYsWEBKSgqpqalkZGRc0C4tLY20tDSWL1/eofuUlJQwdepU0tLSeP/99ztV63PPPcdjjz12wWu5ubkcP36cWbNmUVJSQnp6OtOmTeOee+7B4/EAsHDhQm666Saee+45ABYvXszGjRspKyvrVB1tCVYAKgfCG7+Oau0+xpgBwEvAQx25rqeJcDv1GLyIiATdkiVL2LZtGw8++CAvvfQSAMuXL+fjjz/m2WefJScnp7ldZmYmmZmZPP744x26R3Z2NjfffDOZmZncc889LbapqKggMTGRp59+GoAvvviClJQUqqqqeOqpp0hPT2fSpEkXXLN27drmUPTGG2/wr//6r3zyyScMGTKEP//5z7z33nvU19fz+eefc+TIEQ4dOgTA3Llz2bBhQ4d+Bl8EK2Ds5Lvpq4lA7sUNGhc9/wH479baY75e1xOFuTQFJiIiXaeoqIjw8PDm7+Pi4rjrrrvYtm2bz33U1NRw//33c9tttzFnzhw8Hg+//vWvWbRoEa+//jppaWm0tswkMjKSnJwc1q9fT2VlJQ899BCrV68mIyODLVu28M4777By5coLrjl8+DBjxowB4Be/+AU//OEPASgoKGDQoEFkZmby05/+FIBp06axfft2ACZPnszu3bt9/+X4KCTgPXptAD4zxgwF0oH7jDHPWWvPf7JrITAJWGKMWQL8toXrJgepvoBSABIR6TtKN22i9uSpgPbpShhCTHp6u+2ef/55XnnlFZKTk1mxYgWLFy9ufi8uLo7i4uLmdqtWrWLs2LGsWLGixb4yMjIYP34869evZ+nSpbz66qssXryYiRMnkpmZydKlS9usJS4ujoiICBYuXMi8efNISUkhJSWFRYsW+fxzf/755xQVFTF58mQyMjJITEwEYMCAAc1rhcLDw6mqqvK5T18FJQBZa0uNMWnAD4FfWWtPAdkXtfkt3tBzgYuuKwlGfYEW4XJSU9eAtRZjTHeXIyIil6klS5Ywd+7cFt8rLCwkKSmJM2fOtNmuyb59+5g1axbgHWXZtGlTh+uZMGECJ0+e5I033mi3bXh4OOXl5URFRTXX+8QTT/Duu+8CEBUV1Rx0ysvLaWjwnrF59OhRkpOTO1xbe4I1AoS1tojvnugK+nXdKdztxFqorm0g3O3s7nJERCSIfBmp6WrFxcVs2rSJJ598kjfffNOna8aNG0dWVhZ33HEHWVlZjBs3rkP3LCgoYOvWrTzzzDM4HO2vqJk+fTrvvvsu8+fPx+Px8JOf/IR///d/58orrwTg+uuvZ/v27UyePJns7GxGjRoFwNtvv93qWiR/BC0A9SVh5x2IqgAkIiJd6YknniA0NJRly5YxevRon697+OGHWbBgAVOmTCE5Obl5QbOvFi5cyNSpU8nOzm6/MTBjxgzuvfde0tPTeffdd9m1axfPP/88zz//PD//+c+ZOXMmt956K/n5+WzatImsrCwOHjzIiRMnmDBhQodq84Wx1ga8066Umppqd+zY0a017MsvZW3WMR77wVUkxUZ0ay0iIhJ4+/fvb17AK/Dyyy/z6aef8sILL5Cens6ePXt8ui4vL49t27Yxe/bsFt8vKipi8+bNTJkyhSFDhrBy5Upmz55NTExMi+1b+ncxxuy01qa2V4tGgAKgadSnurahmysREREJrkOHDvHiiy+SlZVFbGwsCQkJTJs2rdWdn8+XlJTUavgBiI2NbX4SDODRRx8NSM0tUQAKgOYDUfUkmIiIXOZGjhzJgQMHmr/fvHlzG617rl6x0WBP1xSAdB6YiIhI76AAFABhbu+vscW9gKyFOk8XVyQiIiJt0RRYALidDhymhSmwykLIXg+FR2H8v8AVk0H7BImIiHQ7BaAAMMZceB6YtXD877D3fe/X/RIh5004ewAm3Auu8LY7FBERkaBSAAqQC47DOLIV9v0R4q6GlDkQHgvfbIEDH0FJHtz6b+AK696CRUSkQ7Tbf8/i7zY+WgMUIGGuxhEgayF3Owy4Cm56HCIGeKe9Rv4QvvdzqCiAQx93d7kiItIBYWFhnDt3zu8/uhIY1lrOnTtHWFjnBxM0AhQgEW6n9ymwc4eh8hyMmn7pep/4ayD5e3DkL3DFzRAV3z3FiohIhyQlJZGXl9fq6ejS9cLCwkhKSur09QpAARLuclJY4YHjX0BIGAxpZdvu0TMg/0vYtwFufKRrixQRkU5xuVwMHz68u8uQANIUWICEuZx4qivhZDYMnQQh7lYaxsA10+D0Hjizv2uLFBEREUABKGDC3U4GlO7D1nkg+ca2Gw9Pg8h471NiDTo+Q0REpKspAAVIuMvJFeVfUR8xEGKHtd3YGeKdCis/Dae/6pL6RERE5DsKQAESXV/IAM8JahJu9G2zwyETIKy/94kxERER6VIKQAEyoOgrwFAWn+LbBQ4HDLsFzh6EslNBrU1EREQupAAUIBGVJyh1xVNpIn2/6IrJ4AjRKJCIiEgXUwAKkLCqk5S44qmu7cCi5tBoSEiBvC+gtjp4xYmIiMgFFIACoboUV20Fxa5BVNXWdezaYbdAXTWc2BGc2kREROQSCkCBUHqCEIehxD2YKk8HH2uPHQb9krzTYNpiXUREpEsoAAVCyQmcDkOpe9B3B6L6yhgYdiuUnYSi3KCUJyIiIhdSAAqE0jxMxACc7siOByDwrgNyuODEzsDXJiIiIpdQAAqEkhPQL5Ewl4NqTycCkCsMBo+D/N3Q0InrRUREpEMUgPxVVwMVBRCTRGRoCOU1HVwE3SQpFTzlUHAgsPWJiIjIJRSA/FWaD1jol0h0mB8BKH4MuCI0DSYiItIFFID8VZLn/RyTSKTbjwDkDPGuBTqV4x1VEhERkaBRAPJXaT64IiE8lqiwECpq6rCdfZw9KRXqPXBKB6SKiIgEkwKQv0qOQ79EMIbo0BAaLFR0ZiE0wIAREB6raTAREZEgUwDyR0ODd/+emEQAosJCAKjo7DSYMZB4PRR8DTVlgapSRERELqIA5I/y09BQ593JGYgK9QagsupOBiCAoZPANmgaTEREJIgUgPxResL7uWkEqDEAdXohNEDMUIiMh/wv/a1OREREWqEA5I/SE+AIgajBwHdTYOX+jAAZ430a7Nwh8FQEokoRERG5SNACkDHmd8aYz40xz7TRZrAx5rPzvk80xuQZYzIbP+KDVV9AVJ6D8AHg8P4aw11OnA4or6n1r9+EiZoGExERCaKgBCBjzCzAaa29CRhhjBnZQptYYA0Qed7L3wOet9amNX4UBKO+gKkq8j611cgY07gbtJ/HWfRLgog4TYOJiIgESbBGgNKAtxu//gS4pYU29cC9QOl5r00GHjbG7DLG/K/WOjfG/MwYs8MYs6OgoBszUlUxhPe/4KXo0BDKq/0cAWqaBjt7ADyV/vUlIiIilwhWAIoEGlcIUwgMvriBtbbUWlty0cub8IanG4CbjDETWurcWvuKtTbVWpsaH99Ns2T1dd5H1c8bAQKoEDsSAAAgAElEQVTvQmi/FkE3aZoGO73H/75ERETkAsEKQOVAeOPXUR24z9+stWXW2npgN3DJ1FmPUVMKWAi7cAQoKsxFWSACUP8rvOFK02AiIiIB124wMcaEXvR9iDHmoXYu28l3014TgVwf6/nYGJNgjIkApgE9d/ijqsj7+aIpsKhQp3/HYTQxxjsKVPC1psFEREQCrM0AZIxxAtuMMc8arwXAfwXuaaffDcA8Y8yLwE+BvcaY53yo51lgK5AFrLTWHvDhmu5RVez9fMkUmIv6Bqiq9XMhNHjXAdl6OLPP/75ERESkWUhbb1pr640xVcBhYCZwHfCfeBcrt3VdqTEmDfgh8Ctr7Skgu5W2aed9vRUY3YH6u0914wjQJVNg3+0FFOFu89fbvthhEBrjPSE+KdW/vkRERKSZL2tzLN4FzR8BscALja+1fZG1RdbatxvDz+WnqhhCwsEVdsHLAdkNuokxMGQCnNkPdR7/+xMRERGg/Smwe/GGnWTgTeBlwA0kGmN+aoyZHfwSe6iqokvW/wBEhwUwAAEkTIB6j3ctkIiIiAREeyNAg4ErgBF4n8j6v4BoIAxIAJKCWl1PVlV8yfofgMjQAByHcb64q8EV4Z0GExERkYBoMwBZa/83cBw4AlQAvwNKgMPW2l9ba38V/BJ7qOriS9b/AES6nTgMgXkUHsDhhMHj4fReaAjAwmoRERHxaQ2QAygA5gP/BDwc1Ip6g/pa8JS3OALUfBxGoEaAwDsNVlsJ574JXJ8iIiJ9WHtrgELwbmh4I3AU7/EWz/PdJod9U/Mj8JeOAIF3IXSFJ4ABKH40OEPhpKbBREREAqG9EaAoa+2N1tr/B+8j8yeBp4C3jTG3tnXS+2WtquVH4JtEhYZQFsgRIKcLBo2GU9ng7waLIiIi0m4Aev+8r8cD84AI4CugGrg1SHX1bNUtb4LYJCosQOeBnS9hovfssaKjge1XRESkD2p3pz5jzDuAE4jBG35G4D3BvRDICGp1PVU7U2DRjWuArLUYYwJzz0HjwBHinQYbMCIwfYqIiPRR7Y0AGbxHWRzCO/31MfBnYBgwEPhTMIvrsaqKwB3lnZpqQWRoCHUNlpq6hsDd0xUGA6/xPg6vaTARERG/tBeA/gD8LyAeqMX7KHwW3kfhy4F1Fx+W2ie08gh8k6bNEAO6Dgi802CV56D0RGD7FRER6WPaC0Dj8B6BMRp4DkhvvCYbqAH+i7W2JqgV9kSt7ALdpF+4d2SopCrAx1cMHgcYPQ0mIiLip/YC0JfAL4BvgV8CRcBqvIuff4o3BPU9rewC3aR/hBuA4srawN43NBrirtKu0CIiIn5qLwDtB/43MAh4FxgFbMJ7IOrPgOFBra4nqq2Guqp2R4CMCUIAAu80WNlJKD8T+L5FRET6iPYC0C3A9/Ge+TW/8fMCvDtCpwG3BbG2nqnpEfiw1keAnA5DdFgIxVVBCEBDrvV+Ppkd+L5FRET6iDYfg7fW/rsxxgkctNb+sXHB80PASWvthi6psKdp2gSxjREggNgIN8WVAV4DBN6pt/5XeAPQyB8Gvn8REZE+oN2zwKy19dbaPzZ+XWOt/W2fDT9w3h5ArY8AAfQPdwVnCgy802Alx6GyMDj9i4iIXOZ8OQxVzlddDBgI69dms/4RLkqqarHB2LNnyETvZy2GFhER6RQFoI6qKobQKHA422zWL9xNXYOlNNB7AQFExUNMIuR/Gfi+RURE+gAFoI7ylIM7ut1msZGNewEFbRosxXsuWNOUnIiIiPhMAaijaivBHdFus9imvYACvRlikwRNg4mIiHSWAlBHeSrBHdlus6bdoIO2EDp6MEQnaBpMRESkExSAOspTDq72A1CYy0m4y0lRMB6Fb5IwEQqPQHVp8O4hIiJyGVIA6ghrG6fA2g9A8N2TYEGTkAJYTYOJiIh0kAJQR9RVg23waQ0QeANQ0KbAAKKHQNRg7QotIiLSQQpAHeGp9H72YQoMvOuAghqAjPFOg509BDVlwbuPiIjIZUYBqCM85d7PPk6BxUa4qaqtp7q2Png1NU2DndQ0mIiIiK8UgDqitnEEqANTYEBw1wHFDIWoIZC/K3j3EBERucwoAHWEp8L72R3lU/P+4d69gIL6JJgxMPQ6OHdYmyKKiIj4SAGoI5oCkMvHEaDIIO8F1CRxEt5pMO0JJCIi4gsFoI6orQSMzwEoOjSEEIehOJgjQABRgyAmCU5oGkxERMQXCkAd4akAVzg4fPu1GWPoF+6iKNgjQACJ10HxMag4F/x7iYiI9HIKQB3hqfD5CbAmcVFuzpbVBKmg8wyd5P2cvzv49xIREenlFIA6wlPh8/RXk/joUM6W12CtDVJRjSIGQOwwPQ0mIiLig6AFIGPM74wxnxtjnmmjzWBjzGfnfe8yxnxojPmrMeahYNXWabUdHwGKjwrFU28praoLUlHnGToJSk9A2ang30tERKQXC0oAMsbMApzW2puAEcaYkS20iQXWAOcniieAndba7wM/NsZEB6O+TvPxJPjzxUeHAlBQXh2Mii409DrAwImdwb+XiIhILxasEaA04O3Grz8BbmmhTT1wL3D+UebnX7cNSG2pc2PMz4wxO4wxOwoKCgJRr286MQU2sDEAnemKdUBhMRA/GvK+8B7cKiIiIi0KCVK/kcCJxq8LgUkXN7DWloL3Sak2rhvcUufW2leAVwBSU1O75i99fR3U1/i8CWKT6NAQQkMcnC0P8qPwTZJSYfda78aIA68OSJeVtZXkluZyrPQYuSW5FNcU02AbALBYYsNiSYxKJCkqiaToJAZHDL7431VERKRHCVYAKgfCG7+OwveRpqbrShqvKw98aZ1U27QLdMdGgIwxxEeHUtAVI0AAQ64FZ6h3FMjPAFRQWcBf8v7CvnP7sFhcDhdXRF/BiP4jcJjv/knPVp3lm6JvyC7wnko/KHwQqUNSmRA/gVBnqF81iIiIBEOwAtBOvNNeWcBE4EAHr3un8bqsoFTXGc0nwXcsAIF3IfSRsxUBLqgVIaHeE+JPfgnX/hicrg53UVRdRObxTL46+xUuh4ubh97MqNhRJEQlEOJo+X8y1lqKa4o5UnKEXad38dHRj9hybAsT4ydyW/JtRLo6tnZKREQkmIIVgDYAnxljhgLpwH3GmOesta0+EdZoDfCRMeZWYCzw9yDV13EdPAfsfPHRoew+XkxNXT2hIc4AF9aCpBsg7x9w6qvGYzJ8t/vMbjYe2YjBMDlhMt9P/L5P4cUYQ2xYLNeHXc/1g6/nRPkJdpzawc7TO8k5m8OUpCncOOTGVgOUiIhIVwrKXyNrbakxJg34IfAra+0pILuVtmnnfX3MGPNDvKNA/8NaWx+M+jqlk1Ng8N2TYOfKPQztH95O6wCIuxrC+kHeDp8DUF1DHX/O/TM7T+9kRL8R3H313cS4YzpdQmJUIolXJ/L9xO/zce7HbD62mZ2nd3LX8LsY0X9Ep/sVEREJhKDtA2StLbLWvt0YfjpyXX7jdSXBqq1TOngQ6vmaH4XvqnVADgckpkLBfqgubbd5qaeUNXvXsPP0Tm4ZegtzxszxK/ycb2D4QOaMmcPs0bMxGNbuX8ufc/9MXUMX7IskIiLSCs1H+KppDVAH9wECGBDpxpguDEDgnQY7/H+8ewJd9YNWm5XUlPDanteoqqviJ9f8hLFxY4NSzsjYkQzrN4wtx7bw95N/J7ckl38Z+S/ER8QH5X4iIiJt0VEYvqqtAEcION0dvtTldBAb4aKgvAsDUEwC9L8Svs1qdU+gitoKXt//OtX11SwYtyBo4aeJy+EifXg69426jzJPGa/kvNL85JiIiEhXUgDyVdNBqJ3c3yY+KrRrDkU93xU3QfkpKMq95K2a+hrW7V9HcXUx94++n4SohC4ra9SAUfx84s9Jik5iwzcb2Hxsc/O+QiIiIl1BAchXngrw41HugdGhFHTFoajnG3qdd0+gby/cTaC2oZY3v36TUxWn+Mmon3BlzJVdV1OjKHcUc8fM5YbBN/C3/L/x5tdvUlPfxQFRRET6LAUgX3kqOvUEWJP4qFBq6y3FlbUBLKodrjBvCMrfDbXes8istfzp8J84VnqMmVfP5JrYa7qunos4HU6mj5jO9OHTOVx8mN999TtKanrW2ncREbk8KQD5qrbjB6Geb0i/MABOlnTBoajnu2Ky9wiP/N0AfFnwJTlnc7gt6Taujb+2a2tpxQ1DbmDO2DmUecr43Z7fUVDZhee7iYhIn6QA5Cs/p8CG9AvDGMgvrgpgUT6IHQbRCfDt55ypPMNHRz5ieMxwbk26tWvraMeIfiOYP24+1lpe3fMqx8uOd3dJIiJyGVMA8oW1fo8AhYY4iY8KJb+kiwOQMXDFZGqLjvLOV68R6gzlnpH3XHCWV08xJHIID41/iAhXBL/f+3sOFR3q7pJEROQy1fP+CvZEtVVgG/xaAwSQ2D+cE109AgSQdAN/rj1Lwdl93DPyHqLd0V1fg49iw2J5aPxDxEfE8+bXb7Lv3L7uLklERC5DCkC+qG06CNW/Az2H9g+ntKqOsuouXAgN7C/7ll3uEG7xwFWRQ7v03p0R6YrkgbEPkBidyLsH32XP2T3dXZKIiFxmFIB80XwQqr8ByLsQOr+46xZC19TXsCl3E4MHjSfN2Q+O/6PL7u2PsJAw5oyZQ3J0Mu8deo8vz3zZ3SWJiMhlRAHIF57OH4R6vqaDULtyIfTWb7dS7innrrGzcQ4YDrnbW90ZuqcJdYYye8xshsUM44PDH7D7zO7uLklERC4TCkC+aJoCc0f51U2Yy8nAKHeXrQM6UX6Cf5z6B6mDU0mOToZht0LFGSg40CX3DwS30839Y+7nqv5X8eHhDzUSJCIiAaEA5AtPufdzJ06Cv9jQ/uFdMgLUYBv40+E/EemKZOoVU70vJqR4Q1zuZ0G/fyC5HC5+OuqnjOg3gg8Of6AQJCIiflMA8oWnEjABC0BFlbVUeur8r6sNfz/5d05VnuLO4XcSFuJde4QzBK68GU7vhYpzQb1/oLkcLu4dfS/D+w3ng8MfkFOQ090liYhIL6YA5IvaSnCFg8P/X1diFyyELveUk3k8k6v7X83YARed8H7lzd69gY7+JWj3DxaXw8V9o+5jWMwwNnyzQU+HiYhIpykA+cJTEZDRH+iahdBbj2+lrqGOO4fdibn49PrwWBg6yXtAatPi7l7E5XRx3+j7uCL6Ct4/9D77z+3v7pJERKQXUgDyRV0NNE0j+SnCHUJshIu8ouAEoILKAnaf2U3qkFTiwuNabnTVVO/5YLl/DUoNwda0MHpo1FDePfQuBwp7z6JuERHpGRSAfFFXDSGhAetuWFwkuecqsEF4HH3Lt1twO93clnRb6436JUL8GO80WH3XbsoYKKHOUOaMmcPgiMH84eAfOFx8uLtLEhGRXkQByBcBHAECGDYwkrLqOs6WewLWJ0BuSS4Hiw5yS+ItRLQ3ZXf17d6n2/K+CGgNXalps8SB4QN58+s3yS3J7e6SRESklwjp7gJ6hfqagI4ADR/o3VH66NkK4qMD06+1ls3HNhPjjuF7Cd9r/4K4q6FfMhz+FJInB2SBd3eIcEUwb+w81uxdw/qv1zN3zFySY5K7u6wOa6ipob6wkPrSUqzHg62pwXo8NHg8GIcD43J99xEaijMmBme/fpiIiEvXeYmISLsUgHxRVx3QEaCBUW6iw0LIPVvBjcMHBKTPPWf3kF+Rz8yrZ+JyuNq/wBjvWqBda+BUDgxNCUgd3SHSFcm8sfNYvXc1b3z9Bg+MfYChUT3zzDNrLXVnzuA5dozavBPUnTtLfWERDRWdW5Bu3G6c/foRMjCOkIQEXAlDcQ1NwBndcw+8FRHpCRSAfFEb2DVAxhiGD4zkyFnvOiB//wu+vqGerce3MjhiMBMGTvD9woQUiPwIDn0CCRO9oaiXinZH88DYB1i9dzVr961l/rj5DIkc0t1lAVBXVET1vn14jhylNu84DVXeLRAcUVGExMcTNmY0ztgBhMQNwBHTD+N24QgNxbjdmNBQaGjA1tZ+91FdTX1JifejuJj6khLqzpyh+usDzcecOKKicA+7ktARI3BfdRUhsbHd+SsQEelxFIDa09AADbUBHQEC70LonLwSiiprGRDp9quvnLM5FNUUcd+o+zoWphwOuOZO2L3WOwqUMNGvOrpbv9B+l4SgQRGDuqWWunPnqN63j+q9+6jNzwcgZOBAwsaNw33FFbiuvBJn//6+/Xs5HJiQEAgPb37JlZh4SbOGmhrqTp2i9uRJak+cwHP0KNV79gLg7N+f0KuvImzMGNzDh3v7ExHpw/T/gu2pa9ywMIAjQAAj4pvWAZUzILLz02B1DXVsy9vG0MihXBN7Tcc7GDoJDn4MBzbBkAm9ehQIIDYslgfGPsCavWuaQ9DA8IFdcm9bV0f1/v1U/v3veL49DoArKYnoadMIGzc26KMwjtBQ3FdeifvKK731WEv92bPUHDmK5+gRqr7aQ+WOnZiwUMJGjSJszBhCR47EuHyYMhURucwoALWnvsb7OcABaFB0KBFuJ0fPVnL9lZ0PQNkF2RTXFDN9+PTOTaU1jwL9Hk5+CUOv63QtPUVceBwPjHuA1XtW8/u9v2f+uPmt74kUAPWlpVTu2EHljp00lJfjjBtA9LRphI8fh7N//6Ddtz3GGELi4wmJjyfyezdi6+qoOXyE6v37qNn/NVXZOZjQUMLHjyP8uutwJSdrQbWI9BkKQO2pC04AMsYwbGAkR8+Wd7qPuoY6Psv7jMSoRK7uf3Xnixl6nXcd0MGPveuCLoM/ggPDB/LAOO9I0O/3/Z4F4xYQGxbYEZj64mLKt22jctcusBB6zUgib7wR99VX98ggYUJCCBt1DWGjrsH+cwOeo0epys7xjgzt3IUzbgARKSmEX3cdzpiY7i5XRCSoFIDa0zwFFtg1QAAjBkayL7+U4koP/SM6vg7oyzNfUuIpYcaIGf79wXU44JppsOv3kL8LEq/vfF89yKCIQcwbO4/f7/s9a/auYf64+QEJQfUlJZR/tp3KnTswxhCRegOR37+5Vy00Ng4HoVddRehVV9Ew4y6q9+6l6stsyv7Pp5Rt3UrY6DFE3Hgj7uHDemSYExHxlwJQe5pHgAIfgEYOigLg61NlTB7RsSmauoY6PjvxGcnRyVzV/yr/ixk6CQ5tga83wpCJ3pPjLwNDIoc0rwnyNwQ1VFdTnplJ5T/+gbWWiEmTiJoyBWe/fgGuums53G4irruOiOuuo66wkMovdlC1axfV+/YREh9PxI03En5dCg63f4v1RUR6kt65+11XCtIiaID46FAGRrn5+mRph6/dfWY3pZ5S0pLSAvNf6MbA2Luh8hzkfuZ/fz3IkMghzB83n5r6GtbsXUNRdVGHrrfWUrlrFwW//t9UfJ5F2IQJxC9aRL8f/ajXh5+LhQwYQMw/TWPQv/1X+t0zE+N2U7pxIwX/+Z+UbdlCfWnH/7cqItITXR7/mR9MdY3HVTgDH4CMMYweEkPWkXPU1NUTGuL06br6hnr+euKvJEcnM7zf8MAVNGi094ywQ59A8o3gjgxc392saSSoo9NhnuPHKd34EbX5+bivSCZm3lxcQ3vmJouBZFyu5lEhz/HjVPz1b5R/tp3yv/6V8PHXEnnLLbgGd88WAyIigaARoPY0jQC5Aj8FBjAmIZq6Bsuh074vhv7q7FeUeEq4NfHWwK/PGHs31FZ5F0RfZhKiEnhg7AN4Gjy8tvc1zladbbVtQ00NJR/+iXMZq6gvK6X/v8xiwMKFfSL8XMydnEzsffcSv3gREampVO/fz9nf/IbCdevwHD/e3eWJiHRK0AKQMeZ3xpjPjTHP+NrGGBNijPnWGJPZ+HFtsOrzWRDXAAFcGRdJuMvJfh+nwRpsA5+d+IyEyAT/nvxqTUwCXDEZcrdDeUHg++9mTSGooaGBNXvXcKbyzCVtag4d4uzy31C5YweRN00mftEiwidO7POLgUMGDKDfXXcx6F//C1E/SKP22Lecy1jFuVdfo+bwYWzjLtQiIr1BUAKQMWYW4LTW3gSMMMaM9LHNBGC9tTat8eOrYNTXIXXVYBzgCM5sodNhGD0kmgOnymhoaP8PyL5z+yisLgzO6E+TUenen3fv+81HK1xOmtYEGQxr9q7hVMUpABqqqih+fwOFa1/HuFzEPbyQmPR0HKGBn/7szRwREUT/4AfE/9d/JebOf6K+8ByFa37PuYxVVB88qCAkIr1CsEaA0oC3G7/+BLjFxzaTgRnGmH80jg51/xqlpoNQg/hf/6MToqnw1HO8qLLNdtZaPsv7jPjweEYPGB20egjrB6PuhDN7vUdkXIbiI+KZP24+IY4Q1uxdw7Gv/srZ3/yGquwviZpyKwN//iju5N53qnxXcrjdRN58M/FPPkm/f/4RDeXlFL3+BudefoXqr79WEBKRHi1YASgSONH4dSEw2Mc2XwB3WGtvBFzA9JY6N8b8zBizwxizo6AgyNM0dTXgDO7jv9cMjsZhYF9+29NgB4oOcKbqDLck3hL86Zjht0FMIux577tpwMtMXHgcC0bNY9iuk+xdsYxiW8nARx4h+o47dDxEB5iQECJSU4lfvIh+M2fSUF1F0br1nP3tb6nev19BSER6pGAFoHKg6eTGqFbu01KbHGvtycbXdgCXTJ0BWGtfsdamWmtT4+PjA1d1S5pGgIIozOVk5KAosvNKWv1j0TT6Exsay/iB44NaDwAOJ1z7Y6gu9p4TdhmqO3uW+tff5aa8CKrHjeAPN1kOhZV0d1m9lnE6iZh0HfGLFtF/1j3Y2lqK1r/JuZUrNSIkIj1OsALQTr6b9poI5PrYZq0xZqIxxgnMBLKDVJ/v6mqCsgfQxSZdGUtJVS2HCypafP9w8WHyK/L5fuL3cZguenhvwAi44mY4+hcoOdF++16kctduzv52JfVFRQyaM4/0R/+dhP7JvHPwHXae3tnd5fVqxuEgPCWF+CeeoP+se2jweChat94bhA4cUBASkR4hWGtsNgCfGWOGAunAfcaY56y1z7TRZjKQA6wDDPCBtXZLkOrzXX1N0EeAAMYkxBDmcrDrWBFXN+4Qfb7tJ7YT445hYvzEoNdyYWEzvOuAstfBLf/qHRnqxazHQ8nGj6javRv38OH0/5dZzedezRszj7cPvs2fjvyJMk8ZtyXd1uef/PJHUxAKmzCB6pwcyjIzKXpjHa6hQ4ma+gPvSfT6/YpINwnKUIK1thTvIucs4AfW2uyLwk9LbUqstXustROstddaa5cEo7YO66IRIJfTwcSk/uzJL6G6tv6C946VHuNY2TFuGnoTIUF6Gq1V7kiY8FMoyfNukNiL1RUUcPaVDKq+/JKotDQGzH/ggkM/XU4X9426j5T4FP6S9xc+PPIh9Q31bfQovmgeEVrUuEaostK7WDpjFTWHDmlESES6RdD+mlpri/juKa9Ot+l2ddVdEoAAJl0Ry9+PFrLnRAmpwwY0v779xHYiQyK5flA3HVKaMBESU70BaNBYiL2ye+rwQ9VXX1Hyxw8wISEMmDeX0Ktb3kPJ6XDyz1f9M/1C+/GXvL9Q5injx9f8mNAg7ATe1xiHg4hJ1xE+4VqqvvyS8r9so3Dt67ivSCbqBz/APWKERoREpMtoJ+j21HXNFBhA8oBw4qPc7Pr2u7Oq8svz+ab4G76X8D1czm58Mmn8v0BoNHz5BtTXdl8dHWTr6ijZuJHiP7yDa8hgBv7i562GnybGGNKS05gxYgZHio/w2p7XKKnR4uhAueCpsR/NoL6khMI1v6fw1VepOXJEI0Ii0iUUgNpibZc8BdbEGMN1V8Zy9GwlBWXeR8+3n9hOmDOMG4bc0CU1tModASlzoPw07Ptj99bio/qyMgpXr6by7/8g8uabGPDggxdMebXn+sHXc//o+ymuKWbVV6s4XqZjHwLJhIQQccMNxC9eTMxdd1FfVETh6jUUvvoaNUeOKgiJSFApALWloQ5sQ5dNgQGkXhlLiMPw12/OUlBZwNeFX3PDkBsI66IQ1qb4Ud79gXI/gxO7uruaNnm+/Zazv11J7clT9P/Jj4m5806Ms+MLuK+OvZqF4xficrhYs3cNXxV0/+bklxsTEkLk9270BqHp06krPEfh6tUKQiISVN2/03JP1nQQahcGoOgwF9dd0Z9d3xZRHXaAEEcIkxMmd9n92zXmn6H4GGS/Cf2SIKpnnQhuraXyH19QuukjnLGxDJj/AK7BLe3D6bv4iHgevvZh/nDwD7z3zXucrDjJHVfe0XXbEfQRxuUicvL3iLh+EpU7d1Gx/TMKV6/GfeWVRKXdpjVCIhJQ+n/wtgT5INTW3DJyIOW1xWw9uoPrB19PhCuiS+/fJmcIXL8AnC7Y8WqP2iXa1tZSsuGPlG7cSOjIkQz82c/8Dj9NIlwRzBkzhxsG38DnJz9n7b61VNS2vGeT+KcpCH03NVboPWts1SqqD+isMREJDAWgtnTDCBDAoOgwXFEHOFNayw2Db+rSe/skPBaumwdlp7wjQT3gD1J9SQnnfvcqVbt3E5WWRuzs2TjCw9u/sANCHCFMHzGdmVfPJK8sj1dyXiGvLC+g95DvGJfLOzX25JP0+9EMGsrKKXrjDc69/DLV+/YpCImIXxSA2tJNI0Dnqs7REHqMGDOKA/k99ImrQaNh9AzI3wUH/9ytpdQcPcrZlS9Td+4csbPvJ3rqD4I6VTIxfiILr12I0zh5bc9r/C3/b/pjHETfLZZu3EeopoaiN9/i7PLfULl7N7ZeezWJSMcpALWlKQAF+TDUi20/sZ3+4aFMGvQ9Mg+eoaauh/4f/NW3Q/JkbwA6/kWX395aS0VWFoVr1uAID2Pgzx4hbPToLrn3kMghPDLhEUYNGMXmY5tZ9/U6TYkFWfNZY088Qf+f/BicDkre30DB//drKrL+jvV4urtEEelFFIDa0jwF1nUjQIXVhTxf7KAAAB0OSURBVOQU5HD9kOu5+9qrKK2q42/fnOuy+3eIMXDtTyBuJGSvh7PfdNmtrcdDyXvvUfrRJkKvuYa4n/2MkGAfjHuR8JBwfnLNT5g+fDpHS47ycvbLHCk+0qU19EXG4SD82msZ+POfEztnDs5+MZR+9BFnXvx/Kft0K/XlCqIi0j4FoLY0jQC5ui4AfZb3GQ7j4PtDv8+wgZGMGxrDXw4WUFbdQ6fCnCGQ+hBExsMXGVB0LOi3rCsq4uyqVVTlfEX07VOJvf9+HGHds02AMYYbhtzAw9c+TGhIKGv3r+WjIx/hqddoRLAZYwgb9f+3d/fBcZx1gse/v+6eV2lG7y+WLNmWHTmx41cSsM2GJMS+DUcSSOoospsDDsIFjuzLLVd7u1vF1dXV7W1t1XLU3nGBAAckEMJVskD2AhwJhIQYHJPYceL4/VW2bL2/zEgz0rx093N/9IwkO7L8opmRLD2fUle/Pd3z6Jme7l8/T7+0U/3ww9R85tP4WpaSeOUV+r/yFeLPP489OE9PHDRNmxd0ADSTfA1QiV6DMLX2J+KPAPCHaxvJOi6/PtJXkjxcE38Ytnzee2/Y7x8v6pvj08ePM/j447jxOFUP/THlt8+PF5Y2ljXyyPpHeN+S9/FG7xt8Y/839IMTS0RE8C9fTvVDD1H7J48SXL+O8X376P+fX2Xo6af1s4Q0TZuWDoBmUuKLoH/T+ZuJ2p+8ukiA97XV8PrpIbrj4yXJxzUJVcHWP/Gul9r9Ne8OsQJSSjH68ssMPfUDjIoKaj73OYLt7QX9jNnyGT7uXn43n1rzKVzl8t0D3+WFjhd0bVAJ+errqfzoR6n7i7+g/AO3kT3bydATTzDw9a8z9uabqOw8rUnVNK3kdAA0EycNhg+M4hdTT7KHdwbe4dbGWydqf/K231RPWcDin/acw3Hn8ZlsuNoLgkRg11chVpgaEDeZZPj7T5F4+RVC69dT89nPYlVXX37BObK8Yjmf3/B5NjdsZnf3br721tc4NnxsrrO1qJiRCJG77qL+P3yRio9+BJQi/tw/0/fl/87Iiy9iDw9ffiWapi1oOgCaiZ0u2TOAXjr7EgEzwG1Lb3vXvLDf4qMbm+mKp3jl6DxuCgMor4Ntf+Y9KPG1/zXrC6Mz584x8PjjZDpOU3HfvVQ8cD+Gv7R35V2LgBngnrZ7+Mzaz+A3/fzwyA959tiz+qWqJSY+H+HNm6n9wheo/jefwr9iOcldu+j/x//B0PefInXsGMp15zqbmqbNAf0qjJmU6EWop2KnOBE7wY5lOwhZ0z+8b01TlE0tlfz6SB83LYnSVFnYh/wVVHk9vP/PYffj8Puvw+ZPwpINV7UKpRRjv3+dkRd+gRmJUvPww/iam4uU4eJpibbwyPpH2NW1i53ndnJs6Bi3Lb2NrU1b8Rm+uc7eoiEiBNraCLS14cTjjO3dy9ievQw/9QPMigpCmzcR3rwZs6JirrOqaVqJyPV+ceAtt9yi9uzZU5yVv/4tGI/B7X9ZnPXjHei/uf+bjNvjPLrp0RkPimMZm3/81XGClsEX7lxF0Hf1L/csqUwSfv8NiJ2FGz8Mq7Z7zWOX4Y6NEXvuOdJHjhJY3U7l/fdjhOfR60CuUSwV45dnf8mhwUNUBirZ3rqdNTVr5sVF3IuRsm1Sh48w/uZe0idPgQiBVasIv2czgfZ2xNLnh5p2PRKRvUqpWy6bTgdAM9j1Ve81D+//s+KsH3in/x1+fOLH3L/qftbXrb9s+tMDSf73zlOsbozwiS3L5v/B08l6zwg6vxeaNsGGPwbr0k1Y6dOnif/oR7hjY0R27CC8Zcv8/x+vUke8g190/ILesV6aypq4q/UuVlSsWHD/5/XEHh5m/M03Gd+3D2dkFCMUIrhuHaGNG/E1N+nvRtOuIzoAKoRX/wECUXjf54qyetu1eeytxwiaQR5Z/8gV72R3nRzg+be7uevGeravKczLPotKKTj5Ehz+KUSbvCaxSOOFSVyXxMsvk3h1J1ZNNZUf+xi+JUvmKMPF5yqXdwbe4ZXOV4ilY6yIruDOljtpibbMddYWNeW6pE+cYPztt0kfPoKybay6OkLr1xFct25eX3yvaZrnSgMgXcc7EzsNZcW7BmhX1y5i6RifuOkTV3WGubWthq5YipeO9FEZ9nHL8nm+Uxbxmr+izbDvKXj1y3DzA9C6FUTI9vYR/8lPyHZ1Edq0ieiH/+V1caHzbBhisKFuA2tr1rK3dy87z+3kOwe/w4roCm5behvLo8t1rcMcEMMg2N5OsL0dN5UidfAg42+9xehLv2b0pV/ja24mtO5mgjffjBmNznV2NU2bBV0DNJMXvwQN62DDxwu+6oHxAR5/+3FWV6/mY+0fu+rlbcfle6+d4UR/go/f0sKGlsqC57EoUnHY9wMYOIqqW0sy2Urid68j/gDRe+8htHbtXOdwTmScDHt797KraxeJbIKWSAvbmrbRXtWOIfpmzbnmxGKMHzhI6sA7ZLu6QQR/y1ICN91EcM0arKqquc6ipmk5ugmsEH7+H2HZVlh7f0FXq5Tie4e+R0+yh0c3Pkq5v/ya1pOxXZ7c1UHHYJIHb21l3dLr5A4WpbD3/jOxHz5Jdmic4C23Ef3Un2OWX1s5LCRZN8u+3n3s6tpFPBOnKlDFliVb2Fi/EX+JX8qrTc8eGGD8wAHShw+T7fYe+Olb0ugFQ6tXYzU26to7TZtDOgCaLaXgp/8e2u+G1R8q6Krf7H2T5089z71t97K5YfOs1pXKOjyxq4OzQ2N8eN0S3r+qtkC5LA6VzZL47W9J7tyJKJvoSkUwGkeq27xAs2rZXGdxXnCVy+HBw+zu3s25xDkCZoD1tevZ3LCZxrLGy69AKwl7eJjUoUOkDh0ie+48KIVZESXQ3k6gfTWBFcuRBd6cq2nzjQ6AZiubgl/8Faz5CKz8YMFWm8gkeOytx2gsa+STaz5ZkDPFjO3yzJ5ODnaNsHVlDfesW4JhzL8z0PTx48R/9jOcoWGC624mevfdXq1P5+tw5HlIj0Lze+DGe7ynSmsAdI52sqdnDwcHD+Ioh6XlS9lUv4mbam665HOjtNJzEgnSx46TPnaU9ImTqEwGsUz8y5bhX7mKwKqVWA0NunZI04pMB0CzNR6DX/1nWP9xWLatYKt99tizHB06yuc3fJ7aUOFqa1xX8fMD3fzuxCCt1WEevLWFqrL5cebpxGKM/OIFUocOYdXWEL3nHgJtbRcmyqa8O8VOvgwoaHmfd+G0DoQmjGXH2D+wn729exkYH8AUk9XVq1lfu56VlSuxDH1Pw3yhbJtMRwfpEydInziJ3ec9wd0oL8e/YjmBFSvwr1iBWV2tAyJNKzAdAM3WaC+88nfeLdvN7ynIKvf07OFnp3/GB1s+OO0rLwrh7c4YP9l3HhG4b0MTG1sq52wH646NkXj1VcZefx0Qyu+4nbJt22Z+wNzYEJz4FZzdDShY+l5ou927fV4DvGvIupJd7O/fz4GBA4zZYwTNIO1V7aypWUNbZZt+yvQ848TjpE+eIn3yBJnTHbiJBABmRRT/8uX4WlrwL1uGVV+vAyJNmyUdAM3W8Bn47Vfg1n8LjTfPenVnR87y5MEnaats449u/KOi3tkzlMzwf944S+fQOCvryvjIxmbqIqV5pxmAm8kw9tprJH77O1QmQ2jjRiJ33oFZeRV3qo0Pw4mXvEDIzUJtOyy/DRrWgjHPn4BdQo7rcDJ+ksODhzkydISUk8Jv+GmraKO9up1Vlave9XJdbW4ppXAGBkifPk3mdAeZs2dwR72AyAgF8S1twbe0Gf/SpfiamxfEU9A1rZR0ADRb/cdg92Ow9U+hdtWsVhVPx/nW/m8RsAJ8dt1nS3Ldhusqfn96iBcP9ZB1XG5dXs0dq+upCBWvZsAdH2dszx6Sr+3GTSQI3LiayF3b8TXUX/tKM0k48xp07IRUDPzlsPRWr4ksunAflHgtbNemI97BkeEjHB8+zkhmBIDGcCNtlW2siK5gWXQZPlPXDs0nSimcWIzsmTNkzp4lc7YTu7/fuxEDMGuq8TU14VvShK9pCb7GRh0UadoMdAA0W937Yc+34QN/CRVLr3k1WTfLEweeYDA1yMM3P0xduK6Amby80VSWlw738UbHEKYh3LK8mm0ra6gtL1yNkBOLkdy9m7E9e1GZDIGVbZTfeSf+1taCfQauA32HoXM39B4E5UJ5IzRt9F60GllyRe8ZWyyUUvSO9XJ8+Din4qfoHO3EUQ6mmDSXN9MaaaUl2kJLpEVfSD0Puek02fNdZM+fJ3v+HNnz53HiIxPzzcpKrMYGfA0NWPUNWA31WLW1iKGfGaVpOgCarc434K2n4M4vQfm1BS22a/Pciec4OHiQB1c/yOrq1QXO5JUbSmb49ZE+3uocxlVwY2OEza1V3NgYwTKvfqepXJfMyZOM7dtH6tAhAELr1lG2bVvxX2GRHoWut6D7LRg8CSgIVUH9Wqi/CWpWgk8f1KfKOBnOjpzl9MhpzoycoTvRjYsLQG2olqayJpZGlrKkbAkN4QZdSzQPuckk2Z4esl3dZLu7sHv7sAcHwPX24WKZmNU1WLW1WHW1WHV1WDU1mLW1GIHSNYFr2lzTAdBsnd4JB/4JdvxXCF79I+9Tdopnjj7D6ZHT7Gjdwbbmwt1JNhsjqSyvnxri9Y4hRlM2Yb/Jzc1R1iypYGVd2WWDIXtwkPF9+xh/+22c+AhGKERo00bKtmy5umt8CiU1Ar0HoO+Q12zppAGByhaoWQVVK6Bq+TV9hwtZ1slyLnGOztFOzifOc370PEk7CYAg1IZqaSxrpD5cT12ojvpwPZWBubugXpuesm3s/n7s3l6yfX3YAwPY/f04Q8MTTWgARlkZVk01ZnUNZlUlVlUVZmUlZlUVRjSqv1dtQdEB0Gyd+BUcfh4+9A8zvr18OvF0nKcPP83A+AD3rbqPDXUbCp+/WXJdxfG+BPvODnOkZ5S07RKwDFbUlrGqvpwVtWU0RoOIQPZ8l/dsk6NHvSffihBYtYrQ5k0EV6+e+a6uUnJsGD4NA8dh8Lh3IbtyvHmhaq8ps6IFKpq9JrNQlW42y1FKMZIZoSvRRe9YL93JbnqSPRPXEQFYYlETqvG6YA3VwWqqglVUBiqJ+vVBdD5Rto09OIQzOOD1hwYn+s5o4oLgCNPAjFZgVuS7KEY0ihmNYkYiGJEIRnm5bl7Trhv6ZaizZedqEq6yKaAj3sGPT/yYjJPhoTUP0VbRdvmF5oBhCKsbI6xujJB1XE71JznSM8LJ3lE6jncSGeqleriX5lgXUTdDOGBR3rac6u3bKd+4YX6+CNK0oPYGrwNwshDvhOEOLxgaOQ89+6ekD0CkAcrqobweymohXOMFS4HIogqORISKQAUVgQpuqrlpYnrKTtE/3s/A+AB9Y30Mjg/Sk+zhyOCRiSY0AFNMb3l/xcR6Iv4IEX+EqD9Kua+csC+s32tWImJZ+Brqp70BQdk2TiyGMzyME4thDw/jxOO4IyNkOjpwRkcmmtUmVygYZWUY5WWY5ZHccLnXD4e9flkZRlkYIxhEgkEdEGvzng6ALsVOgRW84oNgV6KLlztf5kTsBBX+Cj699tM0lDUUOZOzo1wXZ2gIp6+P5v5+6s6fZ0vnOVLxEUbTNiPKord2CQcrmxisb8H2B5FBqNndTXXZINVlfqrL/FSG/FSEfFSEfJQHLcz58hRq0wfVbV6Xl015gdBoD4x2Q6IXBk/A+YtqEQ0fhCq9WqJgBQSiXjNaIOoFR/5yCJSDrwwW8Jlx0ArSEvEulp7KcR1i6RixdIzh1DDD6WHi6TjxdJyT8ZMkMgkUFx5EBSFshSnzlU10YV+YsBUm7AsTskIEzSAhX4iAGSBoBglYAf1MowITy/KuE6qd/kGsynVxEwnc0VGc0VGckRHc0VHcRAInkcBNJLH7+3CTSZTtTP8hhmCEwhihEBIKYgRDSDDgTQsGkEAw188NB/zesH9K3+fTQZRWVEULgETk28Aa4GdKqb+90jRXslxJ2GmwLn3hoFKKWDrGmZEzHB06ypHhI4SsEDuW7eDWxlvnfKetXBeVSuGOjeGOjeGMjOLEY7jxOE487p31DQyibHtiGbOmmsANNxBpbaGptRWrrg4RwXUV/Yk0PfEU/aNp+hNphpIZzgzGSNvuBZ8rAmGfSVnAojxgEfKbhHNdwGcS8pkELIOgz8RvGfhNg4Bl4DMNfJaBZQh+0yjeqzx8Qe8i6ZqVF063MzA26HXjQ7l+zLv1fuC4d+G1usTO3gqCvwyskHfxtS/kTbMC3rAZ8JpRraAXlJkBMP1ejZXhmzKcGzcs71lH83jnbxrmRHPYdBzXIZFNMJoZZTQzSiKbIJFJkMgmSGaTJLNJupJdjGXHSDmpmT9LTIJmEL/pJ2AGCJgBfKYPv+nHb/jxm358hm+yM31YhoXP8PqWWFiGhWmY+AwfppiYhokpJpZhYYiBJV7fEGPRH3TFMLzmr2iUmfZiSilUJoObTHr7mWQSNzmGSo174+PjuGPj3ngyiTs0iBobx02n3l3DNG1GxAuC8sGQ34f4csM+H2JZuWHLa4bPj1vWRIdpIZYJpjk5zTC8YcPwljFz8w1j2j4ii36bWKiKEgCJyAOAqZTaKiLfEZEblFLHL5cGWHe55UomXwMEHB48THeym7STJmWnSDkpupPdjGZGAQiaQW5fejtbm7bivLmf9MndpKeua6brrKbMU0p54/lJykW5rrezUC4ohXJclJ0Fx0U5thfAZLO4mQwqk0Flsl7gk0pN+7ni93sXP1ZUEGhbiVVfn+vqMC7x0kbDEBqiQRqiwYuyrkhlXWLjGWJjWUZTNqOpLIm0TSJtk0zbDCTSjGUcxjMO9pXs9PKfKeAzDUxDsAyZ6BuGYEqunxsWAdMQDBEM8ZpzRJgcxxsXEQSvwiY/DSane+PVCDWI3IAEgABIpfc9mU4Knz2KaSexskksO4lpj2M645jjY5hOGsuJYzg9GE4a08lgOCmEaf7vK9ifKrFADJRhocRAiYkS05sm5sQ0RFBiAIbXv2BcvA8TQZGblxv3MiGTaRAQvPkTaZiS5qKM56Yppsy74EAxORzMdbW5z4BwrvNe/JpWNmmV9To3Q0bZZJRNWtlkVJasipFVDqPKZkjZ2Dhkc31bOWSVc0GT3GwYGBgIteVBLDFy25GBiRccmXgHRANvnldaue0vl0bwtj8QDG9ry41P2R5z8/LllF9XPo33Z+TyJFOLHJlStvlhAaRhrRdMc4l0F213061nYnyGg/7FaYGpXykifsAPVLw7nVJgO0g6C9ksks4gGRsyWSTXkbWRfGc7kBlH7ASkbSThgO3Nw3a8dTleH+cSJylAVbCKoBm85PwZGYIYprfzMASRfJAkIMaU6flx8QKo3O/xgnnTjUvuu5HccvnyzZ8I5oOwKb/nKRvDlHlc8LudmsabddFvdLrf6wXzuSDttNvEFU17d5qy92+b87sTi1UDdAfwTG74ReAPgIsDmenSbLqC5RCRR4BHAFoL+ayZqZa+F7LjABwaPMTBwYNetbwVJGAGWBZZRmu0ldZIK/XhycfX9+3ahTM4VJg8TPxQcj+w3I9DfF4NwcSZjd+P4fcj5eXe2ZI/4LXFh70qaCMcxohEMCsqCto2LyKE/CYhf4glFZe/7TzruKSyDmnb62dsl4zjks662K5L2naxHYXtumQdNTHsuArbVTi5zlUXDzNRE5Wf5sWSXiOMq5QXQypQTM7Lx2NTp+fll83PB3JNOgZKRYBIbtrUZXIDZq7LTTRwsNwMlspgKhtTZbHcLCY2Zq5vKBtDOZjK8YbxhkU5GLgYysFQLkK+706MCy6S+xxRyhtHIcrNHV694NkLfbz5+czn0wKIUjCRZvK/E9TEPze55agpgd2UdBcVyruDv0sHwflD5rU+t9pF4eQ6WyaHHRTOlHFXmBzOfauOKNzcOhTecKsTxjDAyU138baZieHcdO+zve1M4a3bK8nc9jcxnsunmhzPp8mXjMtk+eTnTwwrLprLBcsqAJVETXkn3MXNkJA70Zph/kzTi0aA3AnH5RNaXPLQpRTiKAzHRVyFYef6jss9yz5Ec2QFyvECJeW63gmk43jTXPeivgLXQTnuZF+53vz8PNfNfXH5YTVxwjp58pobn5inwHFx88uqKSe4+ZPgqTsnpkzPpwdvmVwadcGJ89Qd24W/UXXhRnRh+nctM7ncxLLTLXNhsmm/k+mEb70FFmgAVAaczw0PAZuvMM2VLIdS6pvAN8G7C6wwWb7IlNdffGTVR3jghgeuKHCoe/TR6b/wmZadGrnnzxIXYJWrz/SauhbTixmmu8tyxgrBa1jffHRVubzk/3SV/2uh1pNjGTJ9TUfJXEO+DavoTaeX2wavJniaaV2FDsLyTZza/DAf9mXFCoASQL5KoByYbqubLs2VLFdyV/OW7XlzS7g2L0wXyM7u+LTwAmPt+nK5k7OrChr15rxozYeT/GIFGHvxmq8ANgAdV5jmSpbTNE3TNE2blWJVVzwH7BSRJuBDwIMi8rdKqS/NkGYLXp3vxdM0TdM0TdMKqig1QEqpEbyLnHcDdyql3r4o+JkuTXy6acXIn6ZpmqZpi1vRLlhRSg0zeUfXFae5kuU0TdM0TdNmY15cZKxpmqZpmlZKOgDSNE3TNG3R0QGQpmmapmmLjg6ANE3TNE1bdHQApGmapmnaoiPz4XHUsyEi/cCZIq2+Fhgo0rq1SbqcS0OXc2noci4NXc6lcT2W8zKlVN3lEl33AVAxicgepdQtc52PhU6Xc2noci4NXc6locu5NBZyOesmME3TNE3TFh0dAGmapmmatujoAGhm35zrDCwSupxLQ5dzaehyLg1dzqWxYMtZXwOkaZqmadqio2uANE3TNE1bdHQApGmaNgsiUi0iO0Skdq7zomnaldMB0CWIyLdF5DUR+dJc52UhEpEGEdmZG/aJyPMi8jsR+cxc520hEJEKEfl/IvKiiPxERPx6my48EakCfgq8F3hZROp0ORdPbr+xLzesy7nARMQSkbMi8kquWyci/0VE3hCRx+Y6f4WmA6BpiMgDgKmU2gq0icgNc52nhSR30HgSKMtN+lNgr1Lq/cC/EpHInGVu4XgI+IpS6l8APcCD6G26GNYDX1RK/TfgBeCD6HIupi8DIb2PLpr1wA+VUncope4A/MAf4AX4fSKyfS4zV2g6AJreHcAzueEX8TYArXAc4OPASG78DibL+1VgQT50q5SUUl9TSv0yN1oH/Gv0Nl1wSqnfKKV2i8gH8A4Sf4gu56IQkQ8CSbyA/g50ORfDFuAeEXldRL4N3AX8SHl3S70A3DanuSswHQBNrww4nxseAhrmMC8LjlJqRCkVnzJJl3eRiMhWoAroRJdxUYiI4AX0w4BCl3PBiYgf+E/AX+cm6X1GcbwBbFdKvRfwASEWcDnrAGh6CbwvHqAcXU7Fpsu7CESkGvgq8Bl0GReN8jwK7Ae2ocu5GP4a+JpSKpYb19tzcexXSnXnhvewwMt5Qf0zBbSXySrVDUDH3GVlUdDlXWC5M+Zngb9RSp1Bl3FRiMhficgnc6OVwN+jy7kYtgOPisgrwEbgXnQ5F8P3RWSDiJjAR/Fq2hZsOesHIU5DRKLATuAl4EPAlouabLQCEJFXlFJ3iMgy4OfAr/DOoLcopZy5zd31TUT+HfB3wNu5Sd8Fvojepgsqd0H/M0AAOAD8Dd51bLqciyQXBN2H3kcXnIjcDDwNCPB/8Zodd+LVBt0N3K2UOj13OSwsHQBdQm7HtgN4VSnVM9f5WehEpAnvTOMFvSMrDr1Nl4Yu59LQ5VwaIhICPgy8qZQ6Ndf5KSQdAGmapmmatujoa4A0TdM0TVt0dACkaZqmadqiowMgTdM0TdMWHR0AaZqmaZq26OgASNM0TdO0Ref/A0s0qzJT9Or4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "dfs=[\n",
    "(1,(0.65, 0.9999999), ),\n",
    "(4,(0.000001,0.999999), ),\n",
    "(10,(0.000001, 0.99999), ),\n",
    "(20,(0.00000001, 0.9999), ),\n",
    "]# 卡方自由度\n",
    "for df,(l,r) in dfs:\n",
    "    chi2=stats.chi2(df=df)\n",
    "    chi2_x=np.linspace(chi2.ppf(l),chi2.ppf(r),100)\n",
    "    plt.plot(chi2_x,chi2.pdf(chi2_x),alpha=0.6, label=r'PDF of $\\chi^2$({})'.format(df))\n",
    "plt.ylabel('概率')\n",
    "plt.title(r'PDF of $\\chi^2$')\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# t分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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neIEWyXNR7ec3BNiRvL2fRKsuwMwM+CDQCLQBLwCXufsuM/shcBXwy9Tz3P1+4H6A+vp6baMs+Smsy/PMM/u1Z9+q7QczkBAMnTKb6j92X9y69anF7J0a+hYONXv8sIzkIhKlqFp+R4Cq5O3qnp7HEz4DrATeC6x0913Ju5cBYd2lIvmvuRlWrAjG4+ryTDp2ZrDIDdq6mZIDB2LIRiQ6URW/5bzd1TkX2JJ6gJn9rZl9LPlrLXAA+JGZzTWzUuDPgZBPB5EC8NJLwUWsq6sTXY8xaj9pLO11owPxqlUhk/BF8lhUxe9R4Hozuxu4FlhjZnemHHN/8pingVIS1wbvAH4EvAwscfenIspPJF4vvBCM1ddnd25fGDOa5swLhAevfCmGZESiE8k1P3c/ZGYNwOXAN9x9NymtOHdvTN7f1WoSIz5FCtexY4mFrFOFrbEZg6Y586j53W+7xcpf30pp4346hmd5CoZIRCKb5+fuje7+SLLwichxK1cGV06prYXJk+PJJ0X7mJNoP+nkQLxqhVp/Uji0vJlItr34YjA2b15iZZccEdb1WaWuTykgKn4i2dTcDGvWBOPz059KkA3HQopf+c7tlO7fF0M2Ipmn4ieSTatXJ1Z26aqmBqZMiSefHnSMqqPt5HGBeOUaLbokhUHFTySbwro8zzwTSnLvrdg8O7jWZ5WKnxSIqFZ4ESl4fV5Vpa2Nk5cux1pbu4X3jZ1KS4ZWaMmkphmzqXnyv7rFBm3dRMnRI3QOqY4pK5HMyL2vmyIFqnLDK4HC55VVtJyWmwsZtY85iY7hI7sH3alcF3LNUiTPqPiJZEnl2uDeeE0zZsU/sb0nZjTNDO4qput+UghU/ESywZ3KV9YGws0hxSWXhOVXueHVQAtWJN+o+IlkQfnrWyk5krIvXmkZLVOmxZNQmlonnkrn4CHdg+1tVGwIWaFGJI+o+IlkQdh1spYpU/GKihiy6YOSEppnzAqEw7pwRfKJip9IFlStC7neNz1YVHJRaPFbtwZcW2lK/lLxE4lYaeN+ynbvCsSbz5gZQzZ91zz1DCgr7xYrOXaU8u3bYspIZOBU/EQiVhnS6ms7eRydtbUxZNMP5eW0TAlOxwgbwCOSL1T8RCIWdr0vrCsxlzVPmx6IVb66LoZMRDJDxU8kQtbcTMWmjYF48/T86PI8rnlacIf58u3bKDl8KIZsRAZOxU8kQhWbNkBH94WsO2uG0jZuQkwZ9U/HiJG0140OxCs2vBpDNiIDp+InEqGwrsHmadNzau++dIW1/nTdT/KVip9IVNypeDU4GTzs+lk+aDkjpPitfwU6O2PIRmRgVPxEIlK2dw+lB/Z3D1oJLVNOjyehAWqZNBkfNKhbzJqbGLR1SzwJiQyAip9IRCpCujxbJ07CqwbHkE0GlIUvx1b5qro+Jf+o+IlEpHJ9sPi1nH5GDJlkTuiUB133kzwUa/EzsxFmdrmZjYozD5GMa2sLn+KQ98UveN2vbPdOSg4eiCEbkf6LrPiZ2YNmtsTMbu/h/uHAr4FzgD+YWV0654nkg4pNr0F7W7dY55DqvJvikKqztpb2k8YG4prwLvkmkuJnZtcApe6+AJhsZmFbVc8BvuDudwG/BeaneZ5IzqtcHxzl2XL6GXk5xSGVVnuRQhBVy68BeCR5+0nggtQD3P2P7r7UzBaSaP0tSec8ADO72cyWmdmyPXv2ZDh1kYGrCBkE0nx6fk5xSNUcMuWh4rVXoaMjhmxE+ieq4jcE2JG8vR8YE3aQmRnwQaARaEv3PHe/393r3b2+rq4uk3mLDFjp/n2U7U35UmZGy9T8nOKQqnXiqXhlZbeYtbQwaNvWmDIS6buoit8RoCp5u7qn5/GEzwArgfeme55ILqsI6fJsGzeBzuqaGLKJQEkJLacFC3nFa1rqTPJHVMVlOW93Wc4FtqQeYGZ/a2YfS/5aCxxI5zyRXBe6pFmej/JMFTZRX+t8Sj4pi+hxHwUWm9lY4ErgQ2Z2p7t3HcF5P/CImd0ErCZxja8m5bzzIspPJBrt7VRsXB8ItxTI9b7jmqdOY1hKbNDrW7GmYxC4RyT3RFL83P2QmTUAlwPfcPfdwIqUYxqT93eVet7BKPITicqgbVuw1tZuMa+sovWUiTFlFI2OkaPoGD6S0sZ9bwfdqdi4AaaeHF9iImmK7Jqauze6+yPJwhf5eSK5IKzrr3nqNCgpsMvXPQzgqdgQbPWK5KICe0eKxKvytZAuzzxdyLo3zVND1vnUoBfJEyp+IhliTcco374tEG8JKRKFoOW0qYFJ+6X79sLevTFlJJI+FT+RDKnYuAHcu8U6ho+kY8TImDKKlg8eEr5c2zqt9iK5T8VPJEMqXtsQiLWcXpitvuPCuj5Zq10eJPep+IlkSOWGkF3bC/R633GhXbqvaHd3yX0qfiIZUNq4P3G9qyuzxHWxAtZ6yqTA7u4cOwbbgtc+RXKJip9IBlSEjPJsGzseHzwkhmyyqKyM1slTgnF1fUqOU/ETyYCw4leoUxxSNU8J6frUoBfJcSp+IgPlHl78CnSKQ6rQv3PjRmhpyX4yImlS8RMZoLLdOyk5eiQlWE7LxFPjSSjL2kePoXNoynqeHR2wXqu9SO5S8RMZoMqQJb1aJp0K5eUxZBMDs/ApD+r6lBym4icyQGH72LWEXQcrYKF/rwa9SA5T8RMZiPZ2KjZtDIQLfXJ7qtBd6nftgsbG7CcjkgYVP5EBGLRtC7S3dYt51WDaTh4XT0Ix6ayuCf+b1fUpOUrFT2QAKteHrOoydVpgwediENr6eyX4+ojkAhU/kQEo5vl9qVqmnhEMrlsXWOxbJBeo+In0kzUdo3zH64F4sczvS9UyaTKUlnUPHjqUuPYnkmNU/ET6KXQLoxGj6Bg+IqaMYlZenpjikUrX/SQHqfiJ9FNF2Py+sOteRSS0y1fFT3KQip9IP1WGzO8r9C2MehNa/NavT6z4IpJDVPxE+mPfvqLcwqg3beMmwODB3YMtLbB5czwJifRAxU+kP0KG8LeNm1D4Wxj1pqQEpmmpM8l9kRU/M3vQzJaY2e093D/MzB43syfN7D/NbJCZlZnZNjNblPyZHVV+IgMS8mFerFMcAmbMCMZU/CTHRFL8zOwaoNTdFwCTzSysL+g64G53fyewG3gXMAf4qbs3JH9WRZGfyIC4h7b8VPySzgiZ77d5MzQ3Zz8XkR5E1fJrAB5J3n4SuCD1AHf/nrv/d/LXOuBN4DzgPWb2fLLlWJZ6HoCZ3Wxmy8xs2Z49ezKfvciJ7NgBhw93jxXRFka9qquDkSO7xzo7tcWR5JSoit8QYEfy9n5gTE8HmtkCYLi7LwVeAC5z93OAcuCqsHPc/X53r3f3+rq6usxmLtKbsC7PUycXzxZGvTELb/2p61NySFTF7whQlbxd3dPzmNkI4B7gxmRopbsfXw5iGVDcQ+ckN4Ve7yvOVV16NH16MKbiJzkkquK3nLe7OucCW1IPMLNBwM+A29x9azL8IzOba2alwJ8DKyLKT6R/2tthw4ZAuNgntweEtfx27YIDB7Kfi0iIqIrfo8D1ZnY3cC2wxszuTDnmL4H5wBeTIzs/CNwB/Ah4GVji7k9FlJ9I/2zaBK2t3ULFuIVRr2pqYPz4YFy7PEiOCB1QMlDufsjMGoDLgW+4+25SWnHufi9wb8jpc6LISSQjQrruinULo15Nnw7bt3ePrVsH550XTz4iXUQ2z8/dG939kWThEykMYVMcinxVlx71dN1PWxxJDtAKLyLpamoKXaarWLcw6tWUKVCW0rl08CDs1vdhiZ+Kn0i61q8PbmE0fCQdI0b2cEKRq6iAyZODcY36lByg4ieSrrVrAyGN8uyFpjxIjlLxE0lX2GAXze87sbDipy2OJAeo+Imko7ER3nije8yM1tOmxJNPvpg4Eaqquseam2HLlljSETlOxU8kHSGtvraTx9E5pDqGZPKItjiSHKXiJ5KOsCkOut6XHl33kxyk4ifSG3et5zkQYcVv0yZtcSSxUvET6c2uXXDoUPdYWRktk0KG8UvQ6NEwfHj3WGdn6BqpItmi4ifSm7AuuilTtIVRuszU9Sk5R8VPpDdhH9JhuxZIz1T8JMeo+ImcSEdH+A7kYR/m0rOwLws7dwa7k0WypNfiZ2YVKb+XmdmNPR0vUlA2b4aWlu6xwYPhlFPiySdfDR0K40K2fVLrT2JywuKX3FT2aTP7siXcAPxv4C+ykZxI7MI+nKdNS8xfk74Jay1rfz+JyQnfwe7eATQBG0nsrD4P+CnQHn1qIjkgrPipy7N/wl63tWu1xZHEIp2vrw7sAP4LGA58MxkTKWzNzaFbGKn49dPUqVBa2j124EBw2TiRLOit2/ODJArdBODfgfuAQcA4M7vWzD4SfYoiMVm/PjEfrasRI6CuLp588p22OJIc0lvLbwxwCjAZmAp8CqgBKoGTgfGRZicSp7DrUdOnJ+atSf9oyoPkiN6u+X0HeB3YBBwFHgQOAhvd/dvu/o3oUxSJScj+feryHKCw1+/VV4MtbJGIpXPNrwTYA3wcuAK4KdKMRHJBY2NiWbNUYTsUSPomTYLKyu4xbXEkMejtml8ZUAWcA2wGHgHuSsZECldYq2/ChMR8Nem/nrY40pQHybLeWn7V7n6Ou/9foAzYBfwt8IiZXWhmt/d0opk9aGZLejrGzIaZ2eNm9qSZ/aeZDUrnPJGsCCt+M2ZkP49CpOt+kgN6K37/2eX2LOB6YDCwCmgGLgw7ycyuAUrdfQEw2cymhhx2HXC3u78T2A28K83zRKLV2Rle/GbOzH4uhSis+G3cGFxJRyRCZb0dYGY/B0qBoSQK32TgELAfeKCH0xpIdJECPAlcAHTbv8Tdv9fl1zrgTeAjvZ2XzOlm4GaAU7TMlGTa1q1w7Fj32KBBcNpp8eRTaMaMgdraxBy/4zo6ElsczZoVX15SVHpr+RlwLYkCtAv4LfAEMAkYBfy6h/OGkJgYD4kiOabHJzBbAAx396Xpnufu97t7vbvX12nOlWTamjXB2LRpUNbrd0VJR09bHIW97iIR6a34/Qz4ComWWRuJ6Q5LSUx3OAL8W+rC10lHeHtQTHVPz2NmI4B7gBv7cp5IpNTlGb2w11PFT7Kot+Iyk8SyZmcAdwJXJs9ZAbQA/8vdwzrql5PosgSYC2xJPSA5wOVnwG3uvjXd80QidexY+JJmGuySWWGLBbzxBuzdG08+UnR6K34vA38FbAP+AWgEfkBioMu1JApgmEeB683s7uRxa8zszpRj/hKYD3zRzBYll1JLPe83ff6LRAYibML1yJEwenQ8+RSq6mqYODEYV+tPsqS34rcO+A4wGvgPYBrwOInFrW8GTg07yd0PkRj0shS42N1XuPvtKcfc6+7D3b0h+fNwyHkH+/2XifRH2IfvzJla0iwKYYNbVPwkS3q7gn8Bie2LxpNY4WU8cAOJgSktQDmwJOxEd2/k7ZGbaevveSID5q75fdk0cyb8OmXM3CuvQHu7BhdJ5E74L8zdv5rc0Ha9uz+WHNxyI7DL3R/NSoYi2fLmm7BvX/dYSQmccUY8+RS6SZNg8ODu00paWhJz/rSMnESs19GU7t7h7o8lb7ckuytV+KTwhHW5nXoqVGk1v0iUlIS3qtX1KVmgqQQix2mKQ/ZpyoPERMVPBKCtLTHSM5WKX7TCWn7bt3df/UUkAip+IpDYtb21tXtsyBDQ8nnRqq2F8SF7Yoe1wkUySMVPBGDVqmBs5szEdSmJlro+JQZ6Z4u4hxe/2bOzn0sxCit+a9dqd3eJlIqfSNiyWma63pctp50GFSlLBB87pt3dJVIqfiKrVwdjkycnrvlJ9MrKwudShrXGRTJExU9EXZ7xC1vqbOXK7OchRUPFT4pbc3NipGcqFb/sCnu9t2+Hxsbs5yJFQcVPitu6dcGBFcOHw7hx8eRTrIYPhwkTgnF1fUpEVPykuIV9uM6apV0c4hDW+luxIvt5SFFQ8ZPipSkOuWXOnGDslVcSi12LZJiKnxSvbdvg0KHusZ5GHkr0Jk2Cmprusfb2RAEUyTAVPyleYVMcTj89OOdMssMsvNWt634SARU/KV7q8sw9YV2fK1cmuqhFMkjbJUtxOnQofAWRsPlm0ieAr2COAAAWKUlEQVSrth/s97lWM5aTmzuho/3t4NE97HluNW3j+7fI+Ozxw/qdjxQutfykOK1YEWxNjBkDo0fHk48A4JWVtEw+LRCvfEW7PEhmqfhJcXr55WDszDOzn4cENE8PrqlauU67PEhmqfhJ8WluDh9BqOKXE5rPCBa/8h2vU3JQG9xK5qj4SfFZvToxhL6rYcPg1FPjyUe66RgxkvYxJwXi6vqUTIqs+JnZg2a2xMxuP8ExY8xscZffx5nZdjNblPypiyo/KWJhXZ5z52pVlxzSfMaMQKxqjRa6lsyJpPiZ2TVAqbsvACab2dSQY4YD/wp03TfmXOAud29I/uyJIj8pYu3t4VMc1OWZU5pmBKc8VLy2AWs6FkM2Uoiiavk1AI8kbz8JXBByTAfwQaDrEhvnATeZ2Ytm9pWeHtzMbjazZWa2bM8e1Ufpg1dfTVzz66qyEqZNiycfCdV2ykQ6h6ZMUejsUNenZExUxW8IsCN5ez8wJvUAdz/k7qkTgh4nUTjPBhaYWciMV3D3+9293t3r6+rUMyp9ENblOXt2YlkzyR1mNM0Mvv2rVqvrUzIjqnf8EaAqebua9Ivsn9y9BcDMXgKmAvrXLsDAJk8D4M5JzzxPydHWbuHGk6fQNNDHloxrmjWHIUsWd4tVvroOa2nBtQSdDFBULb/lvN3VORfYkuZ5vzWzk81sMPBOIGTxRZH+KX99KyWHUxayLi2jedr0eBKSE2o99TQ6Bw/pHmxvo2L9ungSkoISVfF7FLjezO4GrgXWmNmdaZz3ZeAPwFLg++7+akT5SRGqWhMc6NIyZSpeWRlDNtKrkhKaZwSXm1PXp2RCJN2e7n7IzBqAy4FvuPtuIHRXSndv6HL7D4D2k5FIVIYMlW+aoYWsc1nTrLkMXvZct1jlK2sSo3Z1nVYGILJ5fu7e6O6PJAufSKzKdu+ibG/KyGCz0JaF5I6WKacHru9ZSwsVG9QpJAOjFV6kKFStCo7ybD1lEp01Q2PIRtJWVkbz9JCuT014lwFS8ZPC507VypcC4abZmtieD5pmhUx5WLMKOjtjyEYKhYqfFLyy3bso2/NmIN40e24M2UhftZw+HcrKu8Ws6RgVm16LKSMpBCp+UvDCWn2tkybTOaw2hmykr3zQoNDpKGFd2SLpUvGTwuYe+iHZNEddnvmkaVawlV618mXo6IghGykEKn5S0Mp27wwd5Rm2dJbkrubpM8O7PjXqU/pJxU8K2uAVIV2eE9XlmW+8spKmkB3eB694MYZspBCo+EnhcqcqpPg1zVWXZz5qmjsvEKtcsxLa2mLIRvKdip8UrEFbt1DauK970Cz0+pHkvuZpM4IT3ltbEyu+iPSRip8UrKqXlgViLadN1cT2fFVeHvrFZfDL6vqUvlPxk8LU3s7gkCkOx+afHUMykilNc+cHYpWvrMWammLIRvKZip8UpMr167CmY92DZeU0ayHrvNYy5XQ6h1R3D3a0U7U6dN18kR6p+ElBqnppeSDWNHO2ti/KdyUlNM0JDnwZvPyFGJKRfKbiJwXHmpqoWhvcB/nYvPoYspFMOzY/+P9x0JaNlO7fF3K0SDgVPyk4VatXQEd7t1jnkGpapk6LKSPJpLbxp9A+ekwgPnj58zFkI/lKxU8KTurmp0Ciq6y0NIZsJOPMODb/nEB48IvLwD2GhCQfqfhJQSl78w0Gbd0ciId1lUn+OjbvLDDrFitt3MegLZtiykjyjYqfFJTBy4OtvvaTTqZt/CkxZCNR6RxWS8uU0wNxdX1KulT8pHB0dISO+jtaf16glSD5L6zrs2rlS1hzcwzZSL5R8ZOCUfnqWkqOHO4eLCmlad5Z8SQkkWqeOTt0ubMqLXYtaVDxk4Ix+IVgl2fzjFnBSdFSEHzQIJrODH6xGfL8khiykXwTWfEzswfNbImZ3X6CY8aY2eIuv5eb2a/M7FkzuzGq3KTwlBw6SOUrawPxo2efF0M2ki1Hzz0/ECvf8TrlO16PIRvJJ5EUPzO7Bih19wXAZDObGnLMcOBfgSFdwrcAy939HcD7zawmivyk8Ax5fgl4Z7dYx7Baze0rcG1jx4cOZlLrT3oTVcuvAXgkeftJ4IKQYzqADwKHejjvaUDj06V3HR2hH3bHzjoHStSzX+iOnrMgEKt6aZkGvsgJRfXJMATYkby9Hwgsx+Duh9z9YF/PAzCzm81smZkt27NnT4ZSlnxVuXYVJYdS/ilZCUfPCXaJSeFpmjtfA1+kz6IqfkeAquTt6j48T1rnufv97l7v7vV1dXUDSlTyX/WSZwKx5hmz6KytjSEbyTavqAgd+FK95Bmt+CI9iqr4Leftrs65wJaIz5MiVfbGbgZtei0QP7ogrKddClXYwJey3TsZtHljDNlIPoiq+D0KXG9mdwPXAmvM7M40zvtX4Mtm9m1gBhAcuy7SxZClzwZi7aPqaDktMMZKCljb2PG0Tjw1EK9+9ukYspF8EEnxc/dDJAavLAUudvcV7h465cHdG7rc3gpcDjwLXObuHVHkJ4XBmpoY/GJwOaujCy7Qii5F6Oj5CwOxyrWrYJ+2OpKgyIbCuXujuz/i7rv7eN7O5Hmpg2FEuhny/BKspaVbzMvLOTb/7Jgykjg1zZpDx7CU67zu8Ic/xJOQ5DSNA5f81N5O9bN/DISPzT8HrxocQ0ISu9JSjp4Xcq33mWcg5UuSiIqf5KWqVS+HTG8wjlzYEEs+khuOnrsAysq7B5ua4NngtWEpbip+kn/cqX462JXVPGM2HaM09aWY+eAh4Xs3PvkkdGgIgbxNxU/yTsXGDZTv2hGIH7nw4hiykVxz5B0XBYONjfC89vqTt6n4Sd6pXvRUINZ6yiRaJwWHukvxaR9zEs0zZgfv+O1vNeld3qLiJ3ll0JbNVLy2PhDXtT7p6nDDpcHgrl3w8svZT0Zykoqf5JWa3/82EGsfVUfzzDkxZCO5qu2USbROnhK844kn1PoTQMVP8kj5ti1UrH8lED98yTu1e4MEHG64LBjcsgXWrMl6LpJ79IkheWPo758MxDpGjApd1FikZeo02saOD97x6KNq/YmKn+SJrVupCNmp/fAll6vVJ+HMOHzZFcH466/r2p+o+EkecIdf/CIQ7hg+kmPztN+x9Kx5+iyYODF4x2OPQWdn9hOSnKHiJ7lv7Vp4JeRa38WXQWlpDAlJ3jCDP/uzYHzXLnjhheznIzlDxU9yWw+tvvZRdRw765wYEpK8M2MGTA3Z4uqxx6CtLfv5SE5Q8ZPc9vzzsH17IHzoiner1Sfp6an1t28f/P732c9HcoKKn+SutrbEt/PU8ISJNM+aG0NCkremToWZM4Px//ovOHQo+/lI7FT8JHc98UToRqQHr7xam9VK373//cF/N83N8MtfxpOPxErFT3LT3r2J4pei5YwZ4St3iPRm7FhYGNztnWeeCe1al8Km4ie56eGHob29e6yklIPv/vN48pHCcPXVUFXVPeYOP/mJJr4XGRU/yT2rVsHKlYHwkQsvor1udAwJScGoqYF3vzsY37QJFi/Ofj4SGxU/yS3NzfBv/xaM19Zy+JKQ1TpE+urii2HMmGD8F7+Agwezn4/EQsVPcssvfgH79wfjH/gAXlGR/Xyk8JSVwUc/Gow3NSW626UoqPhJ7njlFfjjH4PxM86As7R4tWTQ6afD+ecH48uXw4svZj8fybrIip+ZPWhmS8zs9nSPMbMyM9tmZouSPyHbMUtBammBH/0oGB80CK6/XlMbJPPe/36org7Gf/xjdX8WgUiKn5ldA5S6+wJgspkF1hbq4Zg5wE/dvSH5syqK/CQHPfxwYnpDqmuugVGjsp+PFL4hQ+Daa4Pxo0fhX/9Voz8LXFQtvwbgkeTtJ4EL0jzmPOA9ZvZ8slVYFvbgZnazmS0zs2V79uzJaOISgxdegGefDcanToWGhqynI0XknHNg3rxgfM2a8C54KRhRFb8hwI7k7f1AyNCq0GNeAC5z93OAcuCqsAd39/vdvd7d6+vq6jKauGTZnj2JbqZU5eXwsY+pu1OiZQbXXQdDhwbv+9nPYOvW7OckWRFV8TsCHJ9JWt3D84Qds9LddyVjy4CQpdilYLS1wQMPJKY3pPrQh2C05vRJFtTUJL5opWpvh/vuS3SDSsGJqvgt5+2uzrnAljSP+ZGZzTWzUuDPgRUR5Sdxc0+0+MK+WdfXwzvekf2cpHjNng0XXRSM79sHDz2k638FKPSaWgY8Ciw2s7HAlcCHzOxOd7/9BMecB6wE/g0w4Jfu/lRE+Unc/vu/YenSYHzUqMQcLHV3Soas2p7myM0F76TupbWU79rRPf7cixyp/AmHrrx6wLnMHj9swI8hmRFJy8/dD5EY0LIUuNjdV6QUvrBjDrr7anef4+6z3f2LUeQmOWD16tANaikrg09+Mrj2okg2lJez//ob8crgv7/qP/6Owc/9KYakJCqRzfNz90Z3f8Tddw/kGCkwmzYlrqOEdSN99KMwaVLWUxI5rmPESPZ/MGT1F6D20Z9T8eq6LGckUdEKL5I9O3fCd78Lra3B+y67DBYsyH5OIilaps/k8GXvCt7hnYz4yb9QvnVL1nOSzFPxk+zYuxe+/e3wkXMzZ8L73pf9nER6cPjSKzg2/+xA3FpbGfUv36d8+7YYspJMimrAixSItAcLnEDZnjcZ9cA/UXIo+FhtJ49j75XX4jsPD/h5RDLGjAPXfJDSgweo2Lih+13NzYz653vZe/NnaBs7PqYEZaDU8pNIle3exaj77gktfB0jR7Hvxk/hGuAiuaisjP0f/QTtY04K3GXNTYy6/58YtHlTDIlJJqj4SWQGbd5I3X33UHIk2KrrrBnK3r/8H3TWhKysIZIjvGowe2/6q9BNlK25iVEP3kvlutUxZCYDpeInkah6aRmj/vlerOlY4L7OmqHsvemv6BgxMobMRPqms2Yoez/5GTpGhiyw3t7GiB8+xJA/Pa2J8HlGxU8yq7OToU/8muEP/xg62gN3dwyrZc+nbgntShLJVZ1Dh7Hnk5+lfVTIWsLeybBf/oLan/80sWSf5AUVP8mYkoMHGPXAP1G9KHxhno7hI9n76f9JR9gHiEiO66ytZe+n/ydt4yaE3j94+fPU3XcPpftCtuaSnKPiJxlRuXYVo7/zTQZt3hh6f+spk9jzmc/TMXxEljMTyZzO6hr23vxZWqacHnp/+fZtjP72Nxi87Dl1g+Y4FT8ZEDt2lOH//kNG/PBBSo4eCT2mac489n7yM3RW12Q5O5HM84oK9t1wM0fPDV983Vpbqf35TxPviQMHspydpEvz/KR/OjsZ/MJShv72N5Qc62HLFzMOX/YuDl/yTi1ULYWlrIyDf/EB2saOo/ax/4DOjsAhletWM2bjeg5dfhVHz78QSktjSFR6ouInfeNOxcYNDP3NY8HV77vorK5h/4c/Rutp2pJRCtexc8+n7aSxjPj3H1HauC9wv7W2Muw3jzLkuWc5dMW7YdxCfRHMEeZ53i9dX1/vy5YtizuNgvXWCi/uDNq8kaFPPs6gLeHX9Y5rmTadxvd/WHP4pGhYczO1j/2cqpdO/Fk0cubpcNVVMGeOimAEzGy5u9enc6xafnJiHR1UrVpB9TOLel3P0CurOPDea2iaV683thQVr6yk8YMfpWnGLGof+4/QhR0A2LIFvvc9GDs2sZh7fT1UVGQ1V0lQy0/C7dwJS5aw57//2PMbuYumM+dz8Mr30jmsNgvJieQua2pi6G9/w5Dnng2M+Bw5ZFD3gysr4dxzYeFCGK91QgeqLy0/FT9525tvwsqV8NxzsC3Rytt3NGT7oS7axk3g4NXX0Drp1GxkKJI3yrdvY+jjv+q2MHag+HU1bhzMmwfz5ydahuo96TMVP0lPa2tic9k1a2DFCnjjjcAhPRW/9tFjOHT5lTTPmqs3qUhP3KlY/wpDn/g15bt2nLj4dTV6NMyeDdOmwemngxZ/T4uKnwS5Q2MjvP46bNwIGzYkrj90dp7wtNTi1zZuAkcuvJimOWdCiaaJiqTFnYpX13H6y88m3nt9YQYTJ8KUKTBpUuJn1Ch96QyhAS/FzB0OHEi04t58M/HfHTsS3ZhhG8mmo6SU5ukzOXLBRbROmqw3nUhfmdFyxgy4bEHiS+fixfDCC9DS0vu57olztmx5OzZkSKKb9KSTEj8nn5z4qa3V+zNNKn75xB2OHEkUt7CfxkbYsyfRnZkJEydycMpsmubOp3NIdWYeU6TYHW+9feAD8Pzz8Oyz3QtbOo4ehfXrEz9dlZfDiBHBn2HDYOjQxE9NjXptUPHLHz/4QeKN0hFcSSJjzBJvyjlzEhfeTz6ZoxnYyV1EElalvp8mz4XJcyltbKRyzUqqVq9k0NZNA1gXtBUOHIVNr/d8iBktU6cx9v/8bT+fozCo+OWgwBsEqD3YwuBDTRl/ro5htbSeOpmWKdNonjb97YnpHYAKn0hWdAwfztELLuLoBRdRcuQwFa9toGLjeipe2xC6csyAuONl5Zl9zDwUWfEzsweBGcBv3P3OdI9J57xi1DF02MAfpKyctpNOpm3ceFomnkrrqafRUTtc1whEckhndQ1NZ86n6cz5AJQ27mfQ1i2Ub9/GoO3bKN/xOjbAfQM7a7TIfCTFz8yuAUrdfYGZPWRmU919Q2/HALN7O69Y9aX4eUUF7aNG0z6q7q2ftpPH0T56jPr6RfJMx/ARNA0f8VYxpLOTsr17KNvzBmVvvkH5m4n/lu15A0vzen9HdU1oD1OcZo/PwBf8Poiq5dcAPJK8/SRwAZBaxMKOmZfGeZjZzcDNyV+PmNmrGco7G0YB2u0yfXq9+k6vWd8U3+v1kx8M5Oxcfr0mpntgVMVvCHB8yf/9wPw0j0nnPNz9fuD+TCWbTWa2LN15KKLXqz/0mvWNXq++KZTXK6o+sCPA8SUJqnt4nrBj0jlPRERkQKIqLstJdFkCzAW2pHlMOueJiIgMSFTdno8Ci81sLHAl8CEzu9Pdbz/BMecBHhIrNHnZXRsjvV59p9esb/R69U1BvF6Rre1pZsOBy4Gn3X13usekc56IiMhA5P3C1iIiIn2lASUiIlJ0VPxiYGZjzOyluPPIdWY2zMweN7Mnzew/zSzNzdCKk5k9aGZLzOz23o8W/fvqn0L5/FLxi8c3eXtKh/TsOuBud38nsBt4V8z55KyuKyYBk5MrJsmJ6d9X/xTE55cWts4yM7sEOErizSYn4O7f6/JrHfBmXLnkgQbSWB1J3qZ/X31XSJ9fKn4RMrP7gGldQr8HLgb+gsRUD+ki7PVy9zvMbAEw3N2XxpRaPkhrdSQJ0r+v9CS7hf+eAvn8UvGLkLt/quvvZvZ/gO+5+wHTTgoBqa8XgJmNAO4B3pf9jPKKVkfqB/376pNbKaDPL71Bsusy4DNmtgg408z+OeZ8clrym+bPgNvcfWvc+eQ4rY7UR/r31WcF9fmleX4xMbNF7t4Qdx65zMz+B/AVYEUydK+7PxxjSjnLzIYCi4HfkVwdyd1za8+aHKN/X/1XCJ9fKn4iBUKrI4mkT8VPRESKjq75iYhI0VHxExGRoqPiJyIiRUfFT0REio6Kn4iIFJ3/D55OggzRh6lJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "df=20# t分布的自由度\n",
    "t=stats.t(df=df)\n",
    "t_x=np.linspace(t.ppf(.001),t.ppf(.999),200)\n",
    "plt.plot(t_x,t.pdf(t_x), 'r-',lw=5, alpha=0.6, label=r'PDF of t({})'.format(df))\n",
    "t_rvs=t.rvs(size=10000)\n",
    "plt.hist(t_rvs,density=True, histtype='stepfilled', alpha=0.2)\n",
    "plt.title(r'PDF of t({})'.format(df))\n",
    "plt.ylabel('概率')\n",
    "plt.legend()\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dce85b710>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "dfs=[\n",
    "(1,(0.04, 0.96), ),\n",
    "(4,(0.001,0.999), ),\n",
    "(10,(0.001,0.999), ),\n",
    "(20,(0.001,0.999), ),\n",
    "]\n",
    "n=stats.norm()\n",
    "n_x=np.linspace(n.ppf(0.000001),n.ppf(0.999999),1000)\n",
    "plt.plot(n_x, n.pdf(n_x), label=r'N(0, 1)')\n",
    "for df,p in dfs:\n",
    "    t=stats.t(df=df)\n",
    "    t_x=np.linspace(t.ppf(p[0]),t.ppf(p[1]),1000)\n",
    "    plt.plot(t_x,t.pdf(t_x), label=r'PDF of t({})'.format(df))\n",
    "plt.ylabel('概率')\n",
    "plt.title(r'PDF of t')\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# F分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "dfn,dfd=4,10#第一自由度和第二自由度\n",
    "f=stats.f(dfn=dfn,dfd=dfd)\n",
    "f_x=np.linspace(f.ppf(.001),f.ppf(.999),200)\n",
    "plt.plot(f_x,f.pdf(f_x), 'r-',lw=5, alpha=0.6, label=r'PDF of F({}, {})'.format(dfn, dfd))\n",
    "f_rvs=f.rvs(size=10000)\n",
    "plt.hist(f_rvs,density=True, histtype='stepfilled', alpha=0.2)\n",
    "plt.title(r'PDF of F({}, {})'.format(dfn, dfd))\n",
    "plt.ylabel('概率')\n",
    "plt.legend()\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dccd57550>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "dfs=[\n",
    "    ((1,30),(.2,.99)),\n",
    "    ((30,5),(.00001,.99)),\n",
    "    ((30,30),(.00001,.999)),\n",
    "    ((30,100),(.0001,.999)),\n",
    "    ((100,100),(.0001,.9999)),\n",
    "]# F分布的自由度\n",
    "for (dfn,dfd),(l,r) in dfs:\n",
    "    f=stats.f(dfn=dfn,dfd=dfd)\n",
    "    f_x=np.linspace(f.ppf(l),f.ppf(r),200)\n",
    "    plt.plot(f_x,f.pdf(f_x), label=r'PDF of F({}, {})'.format(dfn, dfd))\n",
    "plt.ylabel('概率')\n",
    "plt.title(r'PDF of F')\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 三大抽样分布与标准正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24dce5a79b0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds=[\n",
    "    (stats.norm(loc=0,scale=1),r'N(0, 1)'),\n",
    "    (stats.chi2(df=4),r'$\\chi^2$(4)'),\n",
    "    (stats.t(df=5),r't(5)'),\n",
    "    (stats.f(dfn=30, dfd=5),r'F(30, 5)')\n",
    "]\n",
    "plt.figure(figsize=(8,4))\n",
    "for d,l in ds:\n",
    "    x=np.linspace(d.ppf(.001),d.ppf(.999),1000)\n",
    "    plt.plot(x,d.pdf(x), label=l)\n",
    "plt.ylabel('概率')\n",
    "plt.title(r'PDF of 三大分布')\n",
    "plt.subplots_adjust(wspace=.1,hspace=.1,left=0.1,right=1,top=.93,bottom=0.05)  \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# python 回归分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一元线性回归实验\n",
    "抽样数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsample=100\n",
    "X=np.linspace(0,10,100)\n",
    "beta=[1,2]\n",
    "e=np.random.normal(size=nsample)\n",
    "X=sm.add_constant(X)\n",
    "y=np.dot(X,beta)+e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "抽样获得解释变量X和被解释变量y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x24dce635ac8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x=X[:,1],y=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过绘制散点图，确定样本的回归函数形式为$y=a+bx$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.973\n",
      "Model:                            OLS   Adj. R-squared:                  0.973\n",
      "Method:                 Least Squares   F-statistic:                     3536.\n",
      "Date:                Sat, 13 Oct 2018   Prob (F-statistic):           1.05e-78\n",
      "Time:                        15:32:44   Log-Likelihood:                -138.02\n",
      "No. Observations:                 100   AIC:                             280.0\n",
      "Df Residuals:                      98   BIC:                             285.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.1259      0.193      5.836      0.000       0.743       1.509\n",
      "x1             1.9818      0.033     59.464      0.000       1.916       2.048\n",
      "==============================================================================\n",
      "Omnibus:                        2.349   Durbin-Watson:                   2.181\n",
      "Prob(Omnibus):                  0.309   Jarque-Bera (JB):                2.343\n",
      "Skew:                          -0.357   Prob(JB):                        0.310\n",
      "Kurtosis:                       2.771   Cond. No.                         11.7\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model=sm.OLS(exog=X,endog=y)\n",
    "results=model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "多元回归分析的案例介绍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 仿真抽样，在实际中，x和y是抽样所得\n",
    "nsample=100\n",
    "x=np.linspace(0,10,100)\n",
    "X=np.column_stack((x,x**2))\n",
    "beta=[1,2,10]\n",
    "e=np.random.normal(size=nsample)\n",
    "X=sm.add_constant(X)\n",
    "y=np.dot(X,beta)+e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 6.386e+06\n",
      "Date:                Sat, 13 Oct 2018   Prob (F-statistic):          5.08e-249\n",
      "Time:                        15:32:44   Log-Likelihood:                -125.20\n",
      "No. Observations:                 100   AIC:                             256.4\n",
      "Df Residuals:                      97   BIC:                             264.2\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.9069      0.253      3.589      0.001       0.405       1.408\n",
      "x1             2.0281      0.117     17.364      0.000       1.796       2.260\n",
      "x2            10.0010      0.011    884.901      0.000       9.979      10.023\n",
      "==============================================================================\n",
      "Omnibus:                        5.324   Durbin-Watson:                   1.857\n",
      "Prob(Omnibus):                  0.070   Jarque-Bera (JB):                7.075\n",
      "Skew:                          -0.167   Prob(JB):                       0.0291\n",
      "Kurtosis:                       4.259   Cond. No.                         144.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results=sm.OLS(exog=X,endog=y).fit()\n",
    "print(results.summary())"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
